{
"query": {
"display": "derivada de $$f\\left(x\\right)=x^{8}\\sqrt{5-3x}$$",
"symbolab_question": "PRE_CALC#derivative f(x)=x^{8}\\sqrt{5-3x}"
},
"solution": {
"level": "PERFORMED",
"subject": "Calculus",
"topic": "Derivatives",
"subTopic": "Derivatives",
"default": "\\frac{-51x^{8}+80x^{7}}{2\\sqrt{5-3x}}",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "$$\\frac{d}{dx}\\left(x^{8}\\sqrt{5-3x}\\right)=\\frac{-51x^{8}+80x^{7}}{2\\sqrt{5-3x}}$$",
"input": "\\frac{d}{dx}\\left(x^{8}\\sqrt{5-3x}\\right)",
"steps": [
{
"type": "step",
"primary": "Aplicar la regla del producto: $$\\left(f{\\cdot}g\\right)'=f'{\\cdot}g+f{\\cdot}g'$$",
"secondary": [
"$$f=x^{8},\\:g=\\sqrt{5-3x}$$"
],
"result": "=\\frac{d}{dx}\\left(x^{8}\\right)\\sqrt{5-3x}+\\frac{d}{dx}\\left(\\sqrt{5-3x}\\right)x^{8}",
"meta": {
"practiceLink": "/practice/derivatives-practice#area=main&subtopic=Product%20Rule",
"practiceTopic": "Product Rule"
}
},
{
"type": "interim",
"title": "$$\\frac{d}{dx}\\left(x^{8}\\right)=8x^{7}$$",
"input": "\\frac{d}{dx}\\left(x^{8}\\right)",
"steps": [
{
"type": "step",
"primary": "Aplicar la regla de la potencia: $$\\frac{d}{dx}\\left(x^a\\right)=a{\\cdot}x^{a-1}$$",
"result": "=8x^{8-1}",
"meta": {
"practiceLink": "/practice/derivatives-practice#area=main&subtopic=Power%20Rule",
"practiceTopic": "Power Rule"
}
},
{
"type": "step",
"primary": "Simplificar",
"result": "=8x^{7}",
"meta": {
"solvingClass": "Solver"
}
}
],
"meta": {
"solvingClass": "Derivatives",
"interimType": "Derivatives",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYrGwFOVnKdpmGzntotIijwGk3hxk9aCfAWodBRxXgUex2qP3yLWbwuf7ykux/+ljNv8//6/nV5O4fb8Xgwi7maqO95Is7YBdcRqXmTH8euc2S/vtDNB6GWteJZBSm7X14g=="
}
},
{
"type": "interim",
"title": "$$\\frac{d}{dx}\\left(\\sqrt{5-3x}\\right)=-\\frac{3}{2\\sqrt{5-3x}}$$",
"input": "\\frac{d}{dx}\\left(\\sqrt{5-3x}\\right)",
"steps": [
{
"type": "interim",
"title": "Aplicar la regla de la cadena:$${\\quad}\\frac{1}{2\\sqrt{5-3x}}\\frac{d}{dx}\\left(5-3x\\right)$$",
"input": "\\frac{d}{dx}\\left(\\sqrt{5-3x}\\right)",
"result": "=\\frac{1}{2\\sqrt{5-3x}}\\frac{d}{dx}\\left(5-3x\\right)",
"steps": [
{
"type": "step",
"primary": "Aplicar la regla de la cadena: $$\\frac{df\\left(u\\right)}{dx}=\\frac{df}{du}\\cdot\\frac{du}{dx}$$",
"secondary": [
"$$f=\\sqrt{u},\\:\\:u=5-3x$$"
],
"result": "=\\frac{d}{du}\\left(\\sqrt{u}\\right)\\frac{d}{dx}\\left(5-3x\\right)",
"meta": {
"practiceLink": "/practice/derivatives-practice#area=main&subtopic=Chain%20Rule",
"practiceTopic": "Chain Rule"
}
},
{
"type": "interim",
"title": "$$\\frac{d}{du}\\left(\\sqrt{u}\\right)=\\frac{1}{2\\sqrt{u}}$$",
"input": "\\frac{d}{du}\\left(\\sqrt{u}\\right)",
"steps": [
{
"type": "step",
"primary": "Aplicar las leyes de los exponentes: $$\\sqrt{a}=a^{\\frac{1}{2}}$$",
"result": "=\\frac{d}{du}\\left(u^{\\frac{1}{2}}\\right)",
"meta": {
"practiceLink": "/practice/radicals-practice",
"practiceTopic": "Radical Rules"
}
},
{
"type": "step",
"primary": "Aplicar la regla de la potencia: $$\\frac{d}{dx}\\left(x^a\\right)=a{\\cdot}x^{a-1}$$",
"result": "=\\frac{1}{2}u^{\\frac{1}{2}-1}",
"meta": {
"practiceLink": "/practice/derivatives-practice#area=main&subtopic=Power%20Rule",
"practiceTopic": "Power Rule"
}
},
{
"type": "interim",
"title": "Simplificar $$\\frac{1}{2}u^{\\frac{1}{2}-1}:{\\quad}\\frac{1}{2\\sqrt{u}}$$",
"input": "\\frac{1}{2}u^{\\frac{1}{2}-1}",
"result": "=\\frac{1}{2\\sqrt{u}}",
"steps": [
{
"type": "interim",
"title": "$$u^{\\frac{1}{2}-1}=u^{-\\frac{1}{2}}$$",
"input": "u^{\\frac{1}{2}-1}",
"steps": [
{
"type": "interim",
"title": "Simplificar $$\\frac{1}{2}-1\\:$$en una fracción:$${\\quad}-\\frac{1}{2}$$",
"input": "\\frac{1}{2}-1",
"result": "=u^{-\\frac{1}{2}}",
"steps": [
{
"type": "step",
"primary": "Convertir a fracción: $$1=\\frac{1\\cdot\\:2}{2}$$",
"result": "=-\\frac{1\\cdot\\:2}{2}+\\frac{1}{2}"
},
{
"type": "step",
"primary": "Ya que los denominadores son iguales, combinar las fracciones: $$\\frac{a}{c}\\pm\\frac{b}{c}=\\frac{a\\pm\\:b}{c}$$",
"result": "=\\frac{-1\\cdot\\:2+1}{2}"
},
{
"type": "interim",
"title": "$$-1\\cdot\\:2+1=-1$$",
"input": "-1\\cdot\\:2+1",
"steps": [
{
"type": "step",
"primary": "Multiplicar los numeros: $$1\\cdot\\:2=2$$",
"result": "=-2+1"
},
{
"type": "step",
"primary": "Sumar/restar lo siguiente: $$-2+1=-1$$",
"result": "=-1"
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Solver",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s731snK5z/nd3Sq/6JpCqiX1XTSum/z5kLpMzXS1UJIew02FKSBoQo9V3G05AlnWtTyCE30rzMlUAIVDyhseMBropKGn5MuXZnb2ZCo/hVsBU="
}
},
{
"type": "step",
"result": "=\\frac{-1}{2}"
},
{
"type": "step",
"primary": "Aplicar las propiedades de las fracciones: $$\\frac{-a}{b}=-\\frac{a}{b}$$",
"result": "=-\\frac{1}{2}"
}
],
"meta": {
"interimType": "Algebraic Manipulation Join Concise Title 1Eq"
}
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Solver",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7VcI2MpaClJgyGWg1EkySKe0se7vRyav6BwUCJZptwG3MwViaLUXkeD+JukROhWdjMvOxDqXzE3/CFO0TFmffHAH2kDe5DGYTz3TrPquGdIhyukSOA/1RgMKO0TMhInPOMabdUggEogUL9RT7PNKh0VQW3Chm7McvYpuS87Y5EFs="
}
},
{
"type": "step",
"result": "=\\frac{1}{2}u^{-\\frac{1}{2}}"
},
{
"type": "step",
"primary": "Aplicar las leyes de los exponentes: $$a^{-b}=\\frac{1}{a^b}$$",
"secondary": [
"$$u^{-\\frac{1}{2}}=\\frac{1}{\\sqrt{u}}$$"
],
"result": "=\\frac{1}{2}\\cdot\\:\\frac{1}{\\sqrt{u}}",
"meta": {
"practiceLink": "/practice/exponent-practice",
"practiceTopic": "Expand FOIL"
}
},
{
"type": "step",
"primary": "Multiplicar fracciones: $$\\frac{a}{b}\\cdot\\frac{c}{d}=\\frac{a\\:\\cdot\\:c}{b\\:\\cdot\\:d}$$",
"result": "=\\frac{1\\cdot\\:1}{2\\sqrt{u}}"
},
{
"type": "step",
"primary": "Multiplicar los numeros: $$1\\cdot\\:1=1$$",
"result": "=\\frac{1}{2\\sqrt{u}}"
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Generic Simplify Specific 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7JOPQ2g2GS9EQptV8nckZSrH6E/qPf7AlxQDX8MXU5OsAlilG71elit3w1IBbYN0P8rEus7TgCihQBF5omOFkJv2RkT96g5Q5jVbn5fyeQzwB9pA3uQxmE8906z6rhnSIHimBRYRqHSWeJkuUPhfTC0fckB6tn+Lslm20bk1NfC+RFXBEVoMC309dBjB0EbJM4Es6agjDQJIYZAr5O37aAQ=="
}
}
],
"meta": {
"solvingClass": "Derivatives",
"interimType": "Derivatives"
}
},
{
"type": "step",
"result": "=\\frac{1}{2\\sqrt{u}}\\frac{d}{dx}\\left(5-3x\\right)"
},
{
"type": "step",
"primary": "Sustituir en la ecuación $$u=5-3x$$",
"result": "=\\frac{1}{2\\sqrt{5-3x}}\\frac{d}{dx}\\left(5-3x\\right)"
}
],
"meta": {
"interimType": "Derivative Chain Rule 0Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYtuiB8si2Rzy29SaC+ZRTlQB562iL4I4GzHU2vCEsUhM1NpEj4yUFTERoeqJRRLYHBPiZ+52xB2X1cQ6EdG5IQOEIlMXowDUR91Kl/SE5coFeeR1OdpCoc1m9nQe8Y8O0mm86F16QV7LwbyCJvoM1LVGJftth69Dsi14RaP9crrmGS+/CIDQ6NOjbVmL1yPD4EBcOpbjNRCXrOpObW+IvrM016fUsl/V2h/+l0zt3S3o"
}
},
{
"type": "interim",
"title": "$$\\frac{d}{dx}\\left(5-3x\\right)=-3$$",
"input": "\\frac{d}{dx}\\left(5-3x\\right)",
"steps": [
{
"type": "step",
"primary": "Aplicar la regla de la suma/diferencia: $$\\left(f{\\pm}g\\right)'=f'{\\pm}g'$$",
"result": "=\\frac{d}{dx}\\left(5\\right)-\\frac{d}{dx}\\left(3x\\right)"
},
{
"type": "interim",
"title": "$$\\frac{d}{dx}\\left(5\\right)=0$$",
"input": "\\frac{d}{dx}\\left(5\\right)",
"steps": [
{
"type": "step",
"primary": "Derivada de una constante: $$\\frac{d}{dx}\\left({a}\\right)=0$$",
"result": "=0"
}
],
"meta": {
"solvingClass": "Derivatives",
"interimType": "Derivatives",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYmXEh6/dOKVl5+UiJ6t4qwxJ8Vk6wvKjVnTtwWT18bQnz7FeFrf3rcM8IZlDz2c0dm5O2bEw0Ql6ne7k1AUriTvz/OzRy6l5fd6++0L3aMbw"
}
},
{
"type": "interim",
"title": "$$\\frac{d}{dx}\\left(3x\\right)=3$$",
"input": "\\frac{d}{dx}\\left(3x\\right)",
"steps": [
{
"type": "step",
"primary": "Sacar la constante: $$\\left(a{\\cdot}f\\right)'=a{\\cdot}f'$$",
"result": "=3\\frac{dx}{dx}"
},
{
"type": "step",
"primary": "Aplicar la regla de derivación: $$\\frac{dx}{dx}=1$$",
"result": "=3\\cdot\\:1"
},
{
"type": "step",
"primary": "Simplificar",
"result": "=3",
"meta": {
"solvingClass": "Solver"
}
}
],
"meta": {
"solvingClass": "Derivatives",
"interimType": "Derivatives",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s79Kg+idP5vLVrjUll6eMdYsUnAVaDXCLQOuynYB+k3fTZGku9zFkxwe1dTH8vycb9BbqPJ4kl+ElAajU+EBTcW1NbbqpyK7JQEZdATEJR51i3CwF9WgU8/+rFW242YnYD"
}
},
{
"type": "step",
"result": "=0-3"
},
{
"type": "step",
"primary": "Simplificar",
"result": "=-3",
"meta": {
"solvingClass": "Solver"
}
}
],
"meta": {
"solvingClass": "Derivatives",
"interimType": "Derivatives"
}
},
{
"type": "step",
"result": "=\\frac{1}{2\\sqrt{5-3x}}\\left(-3\\right)"
},
{
"type": "interim",
"title": "Simplificar $$\\frac{1}{2\\sqrt{5-3x}}\\left(-3\\right):{\\quad}-\\frac{3}{2\\sqrt{5-3x}}$$",
"input": "\\frac{1}{2\\sqrt{5-3x}}\\left(-3\\right)",
"result": "=-\\frac{3}{2\\sqrt{5-3x}}",
"steps": [
{
"type": "step",
"primary": "Quitar los parentesis: $$\\left(-a\\right)=-a$$",
"result": "=-\\frac{1}{2\\sqrt{5-3x}}\\cdot\\:3"
},
{
"type": "step",
"primary": "Multiplicar fracciones: $$a\\cdot\\frac{b}{c}=\\frac{a\\:\\cdot\\:b}{c}$$",
"result": "=-\\frac{1\\cdot\\:3}{2\\sqrt{5-3x}}"
},
{
"type": "step",
"primary": "Multiplicar los numeros: $$1\\cdot\\:3=3$$",
"result": "=-\\frac{3}{2\\sqrt{-3x+5}}"
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Generic Simplify Specific 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7WW9Djej2t2V9XX+YqO13C5pDM1OsLdjd5Ir+Awl+9pVV00rpv8+ZC6TM10tVCSHshgFkMSyGhkcJufVqsMeq9ACqtCxoEdJkzHBdj1Wzq8yzC+0FcPHGky5+f+dHTyvCixpjZyz1hn/Tx95aZo6CSMI6s6snUuXJdXnaTdiXP5m4l5QaJwiF6q4trNKDTakUrg+rB4/0r72LupHQgSAEfA=="
}
}
],
"meta": {
"solvingClass": "Derivatives",
"interimType": "Derivatives"
}
},
{
"type": "step",
"result": "=8x^{7}\\sqrt{5-3x}+\\left(-\\frac{3}{2\\sqrt{5-3x}}\\right)x^{8}"
},
{
"type": "interim",
"title": "Simplificar $$8x^{7}\\sqrt{5-3x}+\\left(-\\frac{3}{2\\sqrt{5-3x}}\\right)x^{8}:{\\quad}\\frac{-51x^{8}+80x^{7}}{2\\sqrt{5-3x}}$$",
"input": "8x^{7}\\sqrt{5-3x}+\\left(-\\frac{3}{2\\sqrt{5-3x}}\\right)x^{8}",
"result": "=\\frac{-51x^{8}+80x^{7}}{2\\sqrt{5-3x}}",
"steps": [
{
"type": "step",
"primary": "Quitar los parentesis: $$\\left(-a\\right)=-a$$",
"result": "=8x^{7}\\sqrt{5-3x}-\\frac{3}{2\\sqrt{5-3x}}x^{8}"
},
{
"type": "interim",
"title": "Multiplicar $$\\frac{3}{2\\sqrt{5-3x}}x^{8}\\::{\\quad}\\frac{3x^{8}}{2\\sqrt{-3x+5}}$$",
"input": "\\frac{3}{2\\sqrt{5-3x}}x^{8}",
"steps": [
{
"type": "step",
"primary": "Multiplicar fracciones: $$a\\cdot\\frac{b}{c}=\\frac{a\\:\\cdot\\:b}{c}$$",
"result": "=\\frac{3x^{8}}{2\\sqrt{5-3x}}"
}
],
"meta": {
"interimType": "Generic Multiply Title 1Eq"
}
},
{
"type": "step",
"result": "=8x^{7}\\sqrt{-3x+5}-\\frac{3x^{8}}{2\\sqrt{-3x+5}}"
},
{
"type": "step",
"primary": "Convertir a fracción: $$8x^{7}\\sqrt{-3x+5}=\\frac{8x^{7}\\sqrt{5-3x}\\cdot\\:2\\sqrt{5-3x}}{2\\sqrt{5-3x}}$$",
"result": "=-\\frac{3x^{8}}{2\\sqrt{5-3x}}+\\frac{8x^{7}\\sqrt{5-3x}\\cdot\\:2\\sqrt{5-3x}}{2\\sqrt{5-3x}}"
},
{
"type": "step",
"primary": "Ya que los denominadores son iguales, combinar las fracciones: $$\\frac{a}{c}\\pm\\frac{b}{c}=\\frac{a\\pm\\:b}{c}$$",
"result": "=\\frac{-3x^{8}+8x^{7}\\sqrt{5-3x}\\cdot\\:2\\sqrt{5-3x}}{2\\sqrt{5-3x}}"
},
{
"type": "interim",
"title": "$$-3x^{8}+8x^{7}\\sqrt{5-3x}\\cdot\\:2\\sqrt{5-3x}=-3x^{8}+16x^{7}\\left(5-3x\\right)$$",
"input": "-3x^{8}+8x^{7}\\sqrt{5-3x}\\cdot\\:2\\sqrt{5-3x}",
"steps": [
{
"type": "interim",
"title": "$$8x^{7}\\sqrt{5-3x}\\cdot\\:2\\sqrt{5-3x}=16x^{7}\\left(5-3x\\right)$$",
"input": "8x^{7}\\sqrt{5-3x}\\cdot\\:2\\sqrt{5-3x}",
"steps": [
{
"type": "step",
"primary": "Multiplicar los numeros: $$8\\cdot\\:2=16$$",
"result": "=16x^{7}\\sqrt{-3x+5}\\sqrt{-3x+5}"
},
{
"type": "step",
"primary": "Aplicar las leyes de los exponentes: $$\\sqrt{a}\\sqrt{a}=a$$",
"secondary": [
"$$\\sqrt{-3x+5}\\sqrt{-3x+5}=5-3x$$"
],
"result": "=16x^{7}\\left(-3x+5\\right)",
"meta": {
"practiceLink": "/practice/radicals-practice",
"practiceTopic": "Radical Rules"
}
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Solver",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s70rfKRht1jS4JhqVnifXwDNwbR2m3LH/9FGJvnTYxZdA2R4JXe2oN+QvDiQq5u/WidYPfXQvX4/bINBB8wSEQ0boWijuGStNON8mWCXU7s1tEkFyRLR03M11bGpdZyLWisiwU9ry+6SKUt0uXNSvnBrNbboAuZbW4ZbYYhsqcvMjFJp+Hd/ke3PqqoTq6CgQrzOjpTpyoG/uYos09D0eh4w=="
}
},
{
"type": "step",
"result": "=-3x^{8}+16x^{7}\\left(-3x+5\\right)"
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Solver",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7yzhhe7UOtYCUB0D5DuC4DEhS76sVM57z8PdWpIH9tFXZScz5iX4TRahQ5GK7/I6NAJYpRu9XpYrd8NSAW2DdD06SsUW29uMFscSW3cunWVmup4g19A5y4ztDs2PnQqEpRJBckS0dNzNdWxqXWci1oiod1jGnjaZyAxE3Mfohv6DQOPwwJqBdy9j2UpDI5C1m7KsNGIuGlJr91GGZbF+9FmKCz4SO5sGMYs5At4ykGTPM6OlOnKgb+5iizT0PR6Hj"
}
},
{
"type": "step",
"result": "=\\frac{-3x^{8}+16x^{7}\\left(-3x+5\\right)}{2\\sqrt{-3x+5}}"
},
{
"type": "interim",
"title": "Expandir $$-3x^{8}+16x^{7}\\left(5-3x\\right):{\\quad}-51x^{8}+80x^{7}$$",
"input": "-3x^{8}+16x^{7}\\left(5-3x\\right)",
"result": "=\\frac{-51x^{8}+80x^{7}}{2\\sqrt{-3x+5}}",
"steps": [
{
"type": "interim",
"title": "Expandir $$16x^{7}\\left(5-3x\\right):{\\quad}80x^{7}-48x^{8}$$",
"input": "16x^{7}\\left(5-3x\\right)",
"result": "=-3x^{8}+80x^{7}-48x^{8}",
"steps": [
{
"type": "step",
"primary": "Poner los parentesis utilizando: $$a\\left(b-c\\right)=ab-ac$$",
"secondary": [
"$$a=16x^{7},\\:b=5,\\:c=3x$$"
],
"result": "=16x^{7}\\cdot\\:5-16x^{7}\\cdot\\:3x",
"meta": {
"practiceLink": "/practice/expansion-practice",
"practiceTopic": "Expand Rules"
}
},
{
"type": "step",
"result": "=16\\cdot\\:5x^{7}-16\\cdot\\:3x^{7}x"
},
{
"type": "interim",
"title": "Simplificar $$16\\cdot\\:5x^{7}-16\\cdot\\:3x^{7}x:{\\quad}80x^{7}-48x^{8}$$",
"input": "16\\cdot\\:5x^{7}-16\\cdot\\:3x^{7}x",
"result": "=80x^{7}-48x^{8}",
"steps": [
{
"type": "interim",
"title": "$$16\\cdot\\:5x^{7}=80x^{7}$$",
"input": "16\\cdot\\:5x^{7}",
"steps": [
{
"type": "step",
"primary": "Multiplicar los numeros: $$16\\cdot\\:5=80$$",
"result": "=80x^{7}"
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Solver",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7oa3UcTQ1JODhdgc5K/ePLXyRHuGw7+tM5METTDj6vVFVOG9wm4cbG+Oc50zif9r9GYWIwq7tMvHsgtxnvOBtjPEKwPomHX0Hj8mZRbHgDhqepZ5NC3dR2tBo+FunQM6D"
}
},
{
"type": "interim",
"title": "$$16\\cdot\\:3x^{7}x=48x^{8}$$",
"input": "16\\cdot\\:3x^{7}x",
"steps": [
{
"type": "step",
"primary": "Multiplicar los numeros: $$16\\cdot\\:3=48$$",
"result": "=48x^{7}x"
},
{
"type": "step",
"primary": "Aplicar las leyes de los exponentes: $$a^b\\cdot\\:a^c=a^{b+c}$$",
"secondary": [
"$$x^{7}x=\\:x^{7+1}$$"
],
"result": "=48x^{7+1}",
"meta": {
"practiceLink": "/practice/exponent-practice",
"practiceTopic": "Expand FOIL"
}
},
{
"type": "step",
"primary": "Sumar: $$7+1=8$$",
"result": "=48x^{8}"
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Solver",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s734RPgUtPOjumKfqlWu/E2PxI6rtl1NtcN/hmtlZD7xY8LIDuLGMJ18Nh77Jpzso6l9OccPYZS6XnwzWS/KVmVl2Roun23GnmQ6pLpfFpxtiI8fmXHJeMJ2n01SlYnKj0JLd1ohke2Wgml78++2zI0g=="
}
},
{
"type": "step",
"result": "=80x^{7}-48x^{8}"
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Algebraic Manipulation Simplify Title 1Eq"
}
}
],
"meta": {
"interimType": "Algebraic Manipulation Expand Title 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s75yqW9zMJDZ/q3tzPR1Nn6y061ljBSPJeENOw2efoSWvhjXA25QZrtgzx4JuGFD/0ezvI1vLdpFNUL/jbMKrFkYEFMST8lDZxn1Yq5HMKVTv6bNQbpCuy0aFjcHrZB7rh5yRnayFHf/RbNJumM5uqeQ=="
}
},
{
"type": "interim",
"title": "Simplificar $$-3x^{8}+80x^{7}-48x^{8}:{\\quad}-51x^{8}+80x^{7}$$",
"input": "-3x^{8}+80x^{7}-48x^{8}",
"result": "=-51x^{8}+80x^{7}",
"steps": [
{
"type": "step",
"primary": "Agrupar términos semejantes",
"result": "=-3x^{8}-48x^{8}+80x^{7}"
},
{
"type": "step",
"primary": "Sumar elementos similares: $$-3x^{8}-48x^{8}=-51x^{8}$$",
"result": "=-51x^{8}+80x^{7}"
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Algebraic Manipulation Simplify Title 1Eq"
}
}
],
"meta": {
"interimType": "Algebraic Manipulation Expand Title 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7WibMeWR71hMQRFY8qkig58az+7uDWdD0Z4a8KvMafusJQJZuTAY5js+oqjdT8kslFOaOub7Tx3oYMuiO4WUhuYX0K5CYImK/dpECBv0CZ44ezFilETfuNygjs0XPkV2hMZN8/MHxtGRs5CxcReVME03uxHRibZEYwtKt0/jvwUU="
}
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Generic Simplify Specific 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s70rfKRht1jS4JhqVnifXwDHiEWdBzcMp+7J02liP9h52XEP6E8UIMc+VNgkOrgibc/InOClqqWtiH9h7DcJ8ILnCQoYlYQ8U+Tfyx0kyzI8jg1aMB+XDtDRnf60+pbfvlna5EUVPd6EkY94pWrYwmPxMgLF5ZcnOvRwXWatDF/7Hwt9LEn7QCBUukJKctfSJKrFO/xgunl4J8HbdVTuk2VCJMPjG+6hFlzHRgwPeqmJtbJ4mdUnnx+U+wnnJmEH+cEVuo1QcuBoh9SVR+00BcI/bgVjnlYKa1M3zQZGD6XgQ="
}
}
],
"meta": {
"solvingClass": "Derivatives",
"practiceLink": "/practice/derivatives-practice",
"practiceTopic": "Derivatives"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "x",
"plotRequest": "y=\\frac{-51x^{8}+80x^{7}}{2\\sqrt{5-3x}}"
},
"showViewLarger": true
}
},
"meta": {
"showVerify": true
}
}
Solución
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Pasos de solución
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