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Problemas populares de Cálculo

derivative f(x)=16x^{1/8}	derivative\:f(x)=16x^{\frac{1}{8}}
y^{''}-4y^'+4y=(12x^2-6x)e^{2x}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=(12x^{2}-6x)e^{2x}
integral de ((12x+30))/(x^2+2x-8)	\int\:\frac{(12x+30)}{x^{2}+2x-8}dx
integral de 1 a 2 de (4y^2-6y-12)/(y(y+2)(y-3))	\int\:_{1}^{2}\frac{4y^{2}-6y-12}{y(y+2)(y-3)}dy
integral de x^2sinh(x)	\int\:x^{2}\sinh(x)dx
derivative f(x)=2x^{-2}-3x^{-7/3}	derivative\:f(x)=2x^{-2}-3x^{-\frac{7}{3}}
integral de 3xsqrt(x-5)	\int\:3x\sqrt{x-5}dx
(\partial)/(\partial x)(arcsin(x))	\frac{\partial\:}{\partial\:x}(\arcsin(x))
derivada de 4x-5	\frac{d}{dx}(4x-5)
taylor sqrt(x^2+2x),1	taylor\:\sqrt{x^{2}+2x},1
(\partial)/(\partial x)(3x^2y^2-4y)	\frac{\partial\:}{\partial\:x}(3x^{2}y^{2}-4y)
límite cuando x tiende a infinity de (1+2/(x+1))^{x+1}	\lim\:_{x\to\:\infty\:}((1+\frac{2}{x+1})^{x+1})
serie de n=0 a infinity de n^{-0.48}	\sum\:_{n=0}^{\infty\:}n^{-0.48}
límite cuando x tiende a 1 de [f(x)+g(x)]	\lim\:_{x\to\:1}([f(x)+g(x)])
derivada de (10x^{ln(10x)})	\frac{d}{dx}((10x)^{\ln(10x)})
(\partial)/(\partial x)(tan(x-y))	\frac{\partial\:}{\partial\:x}(\tan(x-y))
integral de ln(1)	\int\:\ln(1)dx
(x^3+e^y)dy=3x^2dx	(x^{3}+e^{y})dy=3x^{2}dx
y^'+8y=xe^{-8x}	y^{\prime\:}+8y=xe^{-8x}
derivative sqrt(64-x^2)	derivative\:\sqrt{64-x^{2}}
límite cuando h tiende a 0 de-1/(x(x+h))	\lim\:_{h\to\:0}(-\frac{1}{x(x+h)})
(\partial)/(\partial x)(ex^3-y^5)	\frac{\partial\:}{\partial\:x}(ex^{3}-y^{5})
f(x)=x^{e^x}	f(x)=x^{e^{x}}
derivada de 4^{2x}	\frac{d}{dx}(4^{2x})
derivative f(x)=(8x^2+8x+2)/(sqrt(x))	derivative\:f(x)=\frac{8x^{2}+8x+2}{\sqrt{x}}
inversalaplace ((s))/((s-1)^2)	inverselaplace\:\frac{(s)}{(s-1)^{2}}
integral de x^2sin(2x)	\int\:x^{2}\sin(2x)dx
derivada de (ax^2+bx+ce^{(-x)/6})	\frac{d}{dx}((ax^{2}+bx+c)e^{\frac{-x}{6}})
límite cuando x tiende a 7 de (5x)/(x+2)	\lim\:_{x\to\:7}(\frac{5x}{x+2})
límite cuando t tiende a-2 de t^2-6t-16	\lim\:_{t\to\:-2}(t^{2}-6t-16)
y^{''}-2y^'+y=e^tarctan(t)	y^{\prime\:\prime\:}-2y^{\prime\:}+y=e^{t}\arctan(t)
integral de s/(2s+3)	\int\:\frac{s}{2s+3}ds
integral de (x^{1/2}-2)^2	\int\:(x^{\frac{1}{2}}-2)^{2}dx
derivada de-5x+3	\frac{d}{dx}(-5x+3)
y^{''}-24y^'+144y=0	y^{\prime\:\prime\:}-24y^{\prime\:}+144y=0
límite cuando x tiende a-2-de x	\lim\:_{x\to\:-2-}(x)
límite cuando x tiende a 7+de sqrt(x^2-49)	\lim\:_{x\to\:7+}(\sqrt{x^{2}-49})
integral de (2x^5-7x^3+8)	\int\:(2x^{5}-7x^{3}+8)dx
(\partial)/(\partial x)(sin(0.5x))	\frac{\partial\:}{\partial\:x}(\sin(0.5x))
integral de 20-2x	\int\:20-2xdx
integral de i(t)	\int\:i(t)dt
(\partial)/(\partial x)(-x/(sqrt(x^2-y^2)))	\frac{\partial\:}{\partial\:x}(-\frac{x}{\sqrt{x^{2}-y^{2}}})
derivada de (2x^x)	\frac{d}{dx}((2x)^{x})
integral de (\sqrt[3]{x^5}-x)(x+2)	\int\:(\sqrt[3]{x^{5}}-x)(x+2)dx
y^{'''}-8y=0	y^{\prime\:\prime\:\prime\:}-8y=0
derivada de ln(2-5x)	\frac{d}{dx}(\ln(2-5x))
derivada de arctan(x-x^2)	\frac{d}{dx}(\arctan(x)-x^{2})
integral de sin(7x)ln(sin(7x))	\int\:\sin(7x)\ln(\sin(7x))dx
y^'=2(1+y^2)x	y^{\prime\:}=2(1+y^{2})x
derivada de 2x-1-1/x	\frac{d}{dx}(2x-1-\frac{1}{x})
integral de 1/((1-x^2)^{1/2)}	\int\:\frac{1}{(1-x^{2})^{\frac{1}{2}}}dx
(\partial)/(\partial x)(e^{-x/y}+ln(y/x))	\frac{\partial\:}{\partial\:x}(e^{-\frac{x}{y}}+\ln(\frac{y}{x}))
integral de (4x)/(2x^2+3)	\int\:\frac{4x}{2x^{2}+3}dx
integral de 7/(x^2+4)	\int\:\frac{7}{x^{2}+4}dx
t^2y^'+y=sin(t)	t^{2}y^{\prime\:}+y=\sin(t)
derivada de-arcsin((sqrt(a^2-x^2)/a))	\frac{d}{dx}(-\arcsin(\frac{\sqrt{a^{2}-x^{2}}}{a}))
tangent y=x^2,\at x=-3/4	tangent\:y=x^{2},\at\:x=-\frac{3}{4}
derivada de ln\|csc(x-cot(x)\|)	\frac{d}{dx}(\ln\left\|\csc(x)-\cot(x)\right\|)
área y=x^2-2x,y=2-x	area\:y=x^{2}-2x,y=2-x
integral de 3^{4x+6}	\int\:3^{4x+6}dx
(\partial)/(\partial x)(2y+x^2+1)	\frac{\partial\:}{\partial\:x}(2y+x^{2}+1)
laplacetransformación 2cos^2(t)	laplacetransform\:2\cos^{2}(t)
derivative y=ln((x+3)/(x^2))	derivative\:y=\ln(\frac{x+3}{x^{2}})
derivative \sqrt[7]{x}-7e^x	derivative\:\sqrt[7]{x}-7e^{x}
derivada de x^3sqrt(1-x^2)	\frac{d}{dx}(x^{3}\sqrt{1-x^{2}})
serie de n=1 a infinity de (n!)/(3n!-1)	\sum\:_{n=1}^{\infty\:}\frac{n!}{3n!-1}
área y=3x+1,y=13+2x-x^2	area\:y=3x+1,y=13+2x-x^{2}
tangent f(x)=sqrt(2x+1),\at x=1	tangent\:f(x)=\sqrt{2x+1},\at\:x=1
derivada de (2x+\|x\|/(1+\|x\|))	\frac{d}{dx}(\frac{2x+\left\|x\right\|}{1+\left\|x\right\|})
integral de (9x^2-8x+20)/(x^3+4x)	\int\:\frac{9x^{2}-8x+20}{x^{3}+4x}dx
derivative (75x)/(x^2+100)	derivative\:\frac{75x}{x^{2}+100}
derivative sqrt(1-2x)	derivative\:\sqrt{1-2x}
derivada de (x/(2(x^2-1^2-1))^2)	\frac{d}{dx}((\frac{x}{2(x^{2}-1)^{2}-1})^{2})
y^{''}-9y=0,y(0)=6	y^{\prime\:\prime\:}-9y=0,y(0)=6
límite cuando x tiende a 54 de (x^2)/6-9/x	\lim\:_{x\to\:54}(\frac{x^{2}}{6}-\frac{9}{x})
límite cuando x tiende a 2 de 5x^2-2x+3	\lim\:_{x\to\:2}(5x^{2}-2x+3)
integral de 1/(49-x^2)	\int\:\frac{1}{49-x^{2}}dx
derivative 3\sqrt[3]{x}	derivative\:3\sqrt[3]{x}
(\partial)/(\partial x)((x^2+y)e^{3x+4y})	\frac{\partial\:}{\partial\:x}((x^{2}+y)e^{3x+4y})
(dy)/(dx)=3y+y^4	\frac{dy}{dx}=3y+y^{4}
integral de xsqrt(1+x^2)	\int\:x\sqrt{1+x^{2}}dx
d/(dy)(x/(sqrt(x^2+y^2)))	\frac{d}{dy}(\frac{x}{\sqrt{x^{2}+y^{2}}})
límite cuando x tiende a 2 de sqrt(4x-3)	\lim\:_{x\to\:2}(\sqrt{4x-3})
derivada de sin(1/(sqrt(x)))	\frac{d}{dx}(\sin(\frac{1}{\sqrt{x}}))
integral de (xe^x)/2	\int\:\frac{xe^{x}}{2}dx
(\partial)/(\partial x)(ln(x+3y+7z))	\frac{\partial\:}{\partial\:x}(\ln(x+3y+7z))
integral de tan^3(x)(sec(x))^{3/2}	\int\:\tan^{3}(x)(\sec(x))^{\frac{3}{2}}dx
(\partial)/(\partial y)(2y^2+3x)	\frac{\partial\:}{\partial\:y}(2y^{2}+3x)
límite cuando x tiende a 0 de 3/0	\lim\:_{x\to\:0}(\frac{3}{0})
serie de n=0 a infinity de (1/3)^{2n}	\sum\:_{n=0}^{\infty\:}(\frac{1}{3})^{2n}
derivative (5x)/(4x^2+1)	derivative\:\frac{5x}{4x^{2}+1}
integral de x/(x^2+2x+2)	\int\:\frac{x}{x^{2}+2x+2}dx
área Y(x)=x^3-x^2-6x,Y(x)=0	area\:Y(x)=x^{3}-x^{2}-6x,Y(x)=0
derivative f(x)=7sqrt(x)	derivative\:f(x)=7\sqrt{x}
integral de e^{-0.8x}	\int\:e^{-0.8x}dx
(\partial)/(\partial x)(x^2*ln(y))	\frac{\partial\:}{\partial\:x}(x^{2}\cdot\:\ln(y))
derivada de sin(2x-pi/3)	\frac{d}{dx}(\sin(2x-\frac{π}{3}))
(\partial)/(\partial x)(x^3+y^2-yx^2-xy)	\frac{\partial\:}{\partial\:x}(x^{3}+y^{2}-yx^{2}-xy)
d/(dt)(5e^tcos(t))	\frac{d}{dt}(5e^{t}\cos(t))
derivative f(x)=cos(5x)	derivative\:f(x)=\cos(5x)

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