{
"query": {
"display": "derivada de $$3x^{3}$$",
"symbolab_question": "PRE_CALC#derivative 3x^{3}"
},
"solution": {
"level": "PERFORMED",
"subject": "Calculus",
"topic": "Derivatives",
"subTopic": "Derivatives",
"default": "9x^{2}",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "$$\\frac{d}{dx}\\left(3x^{3}\\right)=9x^{2}$$",
"input": "\\frac{d}{dx}\\left(3x^{3}\\right)",
"steps": [
{
"type": "step",
"primary": "Sacar la constante: $$\\left(a{\\cdot}f\\right)'=a{\\cdot}f'$$",
"result": "=3\\frac{d}{dx}\\left(x^{3}\\right)"
},
{
"type": "step",
"primary": "Aplicar la regla de la potencia: $$\\frac{d}{dx}\\left(x^a\\right)=a{\\cdot}x^{a-1}$$",
"result": "=3\\cdot\\:3x^{3-1}",
"meta": {
"practiceLink": "/practice/derivatives-practice#area=main&subtopic=Power%20Rule",
"practiceTopic": "Power Rule"
}
},
{
"type": "step",
"primary": "Simplificar",
"result": "=9x^{2}",
"meta": {
"solvingClass": "Solver"
}
}
],
"meta": {
"solvingClass": "Derivatives",
"practiceLink": "/practice/derivatives-practice",
"practiceTopic": "Derivatives"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "x",
"plotRequest": "y=9x^{2}"
},
"showViewLarger": true
}
},
"meta": {
"showVerify": true
}
}
Solución
derivada de
Solución
Pasos de solución
Sacar la constante:
Aplicar la regla de la potencia:
Simplificar