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Problemas populares de Cálculo

(dy)/(dx)=(10x^2)/(sqrt(1+x^3))	\frac{dy}{dx}=\frac{10x^{2}}{\sqrt{1+x^{3}}}
área x=15-y^2,x=y^2-3	area\:x=15-y^{2},x=y^{2}-3
integral de 0 a pi/8 de arctan(2x)	\int\:_{0}^{\frac{π}{8}}\arctan(2x)dx
(\partial)/(\partial w)(warctan(uv))	\frac{\partial\:}{\partial\:w}(w\arctan(uv))
y^{''}+2y-1(y^')2=y^'	y^{\prime\:\prime\:}+2y-1(y^{\prime\:})2=y^{\prime\:}
serie de n=1 a infinity de 9	\sum\:_{n=1}^{\infty\:}9
límite cuando x tiende a 0-de \|(8x)/x \|	\lim\:_{x\to\:0-}(\left\|\frac{8x}{x}\right\|)
integral de sin((nx)/2)	\int\:\sin(\frac{nx}{2})dx
d/(dt)(e^t-1)	\frac{d}{dt}(e^{t}-1)
integral de (x^4+x)/(x+1)	\int\:\frac{x^{4}+x}{x+1}dx
tangent 2x^3-x^2	tangent\:2x^{3}-x^{2}
laplacetransformación e^{3t}sin(4t)	laplacetransform\:e^{3t}\sin(4t)
integral de sqrt(x^2+x)	\int\:\sqrt{x^{2}+x}dx
serie de n=0 a infinity de 9^n	\sum\:_{n=0}^{\infty\:}9^{n}
derivative f(x)=(x^2)/((x^3)(x^2))	derivative\:f(x)=\frac{x^{2}}{(x^{3})(x^{2})}
integral de 1/(xsqrt(x^2-81))	\int\:\frac{1}{x\sqrt{x^{2}-81}}dx
derivative f(t)=t^4-20t^3+112t^2	derivative\:f(t)=t^{4}-20t^{3}+112t^{2}
tangent f(x)=arccos(x)+x,\at x=0	tangent\:f(x)=\arccos(x)+x,\at\:x=0
t(dy)/(dt)+18y= 1/t	t\frac{dy}{dt}+18y=\frac{1}{t}
tangent f(x)=(2x-1)/(x+3),\at x=3	tangent\:f(x)=\frac{2x-1}{x+3},\at\:x=3
integral de-sin(t)	\int\:-\sin(t)dt
(\partial ^2)/(\partial x\partial y)(ln(3x^2-y^3-3))	\frac{\partial\:^{2}}{\partial\:x\partial\:y}(\ln(3x^{2}-y^{3}-3))
derivada de 9e^{-x}+e^{4x}	\frac{d}{dx}(9e^{-x}+e^{4x})
integral de ((x^3)/(x^2+1))	\int\:(\frac{x^{3}}{x^{2}+1})dx
(\partial)/(\partial z)(\sqrt[3]{xyz})	\frac{\partial\:}{\partial\:z}(\sqrt[3]{xyz})
integral de sqrt(2500-x^2)	\int\:\sqrt{2500-x^{2}}dx
derivada de (2x^2-1^3*(1-x^2)^{-3})	\frac{d}{dx}((2x^{2}-1)^{3}\cdot\:(1-x^{2})^{-3})
derivada de 2+x^2	\frac{d}{dx}(2+x^{2})
derivada de ((x^3+2x^3)/(sqrt(2x-4)))	\frac{d}{dx}(\frac{(x^{3}+2x)^{3}}{\sqrt{2x-4}})
derivative 1/(cos(x))	derivative\:\frac{1}{\cos(x)}
integral de sqrt(2x+4)	\int\:\sqrt{2x+4}dx
integral de (37)/(x^3-125)	\int\:\frac{37}{x^{3}-125}dx
derivative 3x^2sin(x)tan(x)	derivative\:3x^{2}\sin(x)\tan(x)
(dy)/(dx)-y/x =2xe^x,y(1)=2e-8	\frac{dy}{dx}-\frac{y}{x}=2xe^{x},y(1)=2e-8
derivada de \sqrt[13]{9+7\sqrt[5]{2x}}	\frac{d}{dx}(\sqrt[13]{9+7\sqrt[5]{2x}})
integral de (sec^2(θ)+sec(θ)tan(θ))	\int\:(\sec^{2}(θ)+\sec(θ)\tan(θ))dθ
d/(dy)(sqrt(xy))	\frac{d}{dy}(\sqrt{xy})
(\partial)/(\partial y)(2-y-2x)	\frac{\partial\:}{\partial\:y}(2-y-2x)
(\partial)/(\partial x)(x^2ysin(1/x))	\frac{\partial\:}{\partial\:x}(x^{2}y\sin(\frac{1}{x}))
límite cuando x tiende a 0 de-x^3	\lim\:_{x\to\:0}(-x^{3})
derivative f(x)=sqrt(x^2+6)	derivative\:f(x)=\sqrt{x^{2}+6}
integral de 1/(y-yln(y))	\int\:\frac{1}{y-y\ln(y)}dy
maclaurin sqrt(4-3x)	maclaurin\:\sqrt{4-3x}
f(x)=ln(sin(x)+4)	f(x)=\ln(\sin(x)+4)
derivada de 1000(sin(x)(e^{-2x}))	\frac{d}{dx}(1000(\sin(x))(e^{-2x}))
integral de (cos(9x))/(1+sin^2(9x))	\int\:\frac{\cos(9x)}{1+\sin^{2}(9x)}dx
integral de x/(x^2+y)	\int\:\frac{x}{x^{2}+y}dx
d/(dt)(e^{(t^2)/2})	\frac{d}{dt}(e^{\frac{t^{2}}{2}})
integral de 4/(sqrt(x^2-16))	\int\:\frac{4}{\sqrt{x^{2}-16}}dx
derivada de 3x^{4x}	\frac{d}{dx}(3x^{4x})
(\partial)/(\partial x)(x*(e^y)/(x+y))	\frac{\partial\:}{\partial\:x}(x\cdot\:\frac{e^{y}}{x+y})
serie de n=8 a infinity de n/(nln(n))	\sum\:_{n=8}^{\infty\:}\frac{n}{n\ln(n)}
(\partial)/(\partial x)(ln(x+8y+9z))	\frac{\partial\:}{\partial\:x}(\ln(x+8y+9z))
derivative f(x)=((x^2-1))/((x^2+x+1))	derivative\:f(x)=\frac{(x^{2}-1)}{(x^{2}+x+1)}
límite cuando x tiende a 1-de x/(x+1)	\lim\:_{x\to\:1-}(\frac{x}{x+1})
derivada de 2/(5x^2-1)	\frac{d}{dx}(\frac{2}{5x^{2}-1})
y^{''}+(2/x)y^'=0	y^{\prime\:\prime\:}+(\frac{2}{x})y^{\prime\:}=0
(\partial)/(\partial x)(550-0.53N^2)	\frac{\partial\:}{\partial\:x}(550-0.53N^{2})
derivative 2+9sin(x^2)	derivative\:2+9\sin(x^{2})
x^{''}+2x^'+x=0	x^{\prime\:\prime\:}+2x^{\prime\:}+x=0
integral de sqrt(3-2x+x^2)	\int\:\sqrt{3-2x+x^{2}}dx
inversalaplace {(((s+1)^3)/4)^2}	inverselaplace\:\left\{(\frac{(s+1)^{3}}{4})^{2}\right\}
derivada de (88x/(99x-88))	\frac{d}{dx}(\frac{88x}{99x-88})
derivada de cx^3	\frac{d}{dx}(cx^{3})
tangent f(x)=x^4+2e^x,\at x=0	tangent\:f(x)=x^{4}+2e^{x},\at\:x=0
límite cuando x tiende a 1 de x^2+x+1	\lim\:_{x\to\:1}(x^{2}+x+1)
integral de 0 a 4 de (sqrt(x))	\int\:_{0}^{4}(\sqrt{x})dx
límite cuando x tiende a 0 de 4xcos(x)	\lim\:_{x\to\:0}(4x\cos(x))
y^{''}+81y=cos(6t)	y^{\prime\:\prime\:}+81y=\cos(6t)
tangent f(x)=sqrt(5x-1),\at x=2	tangent\:f(x)=\sqrt{5x-1},\at\:x=2
pendienteintercept (1.8)(0.5)	slopeintercept\:(1.8)(0.5)
límite cuando x tiende a 0 de 2/(x^3-x)	\lim\:_{x\to\:0}(\frac{2}{x^{3}-x})
área y=2x^3-13x,y=x^2+6	area\:y=2x^{3}-13x,y=x^{2}+6
límite cuando x tiende a 1-de sqrt(x)	\lim\:_{x\to\:1-}(\sqrt{x})
(\partial)/(\partial y)((x+y)*e^{x+2y})	\frac{\partial\:}{\partial\:y}((x+y)\cdot\:e^{x+2y})
derivative (2x^2-3x+1)/x	derivative\:\frac{2x^{2}-3x+1}{x}
derivative p	derivative\:p
(\partial)/(\partial x)(2xy+y^2)	\frac{\partial\:}{\partial\:x}(2xy+y^{2})
pendiente (-4.5)(1.1)	slope\:(-4.5)(1.1)
derivative sqrt(1-sec(x))	derivative\:\sqrt{1-\sec(x)}
integral de 6x+4	\int\:6x+4dx
integral de (e^{2x})/(e^{2x)+1}	\int\:\frac{e^{2x}}{e^{2x}+1}dx
derivada de (2x^2-13x+20/((x-1)^2))	\frac{d}{dx}(\frac{2x^{2}-13x+20}{(x-1)^{2}})
integral de x^3sqrt(x^2+42)	\int\:x^{3}\sqrt{x^{2}+42}dx
límite cuando x tiende a 1 de (x^2+x)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{2}+x}{x-1})
6t(dy)/(dt)+y=t^5	6t\frac{dy}{dt}+y=t^{5}
derivada de sqrt(1+cos^2(x))	\frac{d}{dx}(\sqrt{1+\cos^{2}(x)})
integral de (x-2)e^x	\int\:(x-2)e^{x}dx
derivative y=2arcsin(3)x^5	derivative\:y=2\arcsin(3)x^{5}
tangent y=5-7x^2,(3,-58)	tangent\:y=5-7x^{2},(3,-58)
integral de (5sin(x))/(cos^3(x))	\int\:\frac{5\sin(x)}{\cos^{3}(x)}dx
integral de (x^2)/2	\int\:\frac{x^{2}}{2}dx
integral de 0 a pi de sin^2(2x)	\int\:_{0}^{π}\sin^{2}(2x)dx
límite cuando x tiende a 4 de 3-x	\lim\:_{x\to\:4}(3-x)
y^'=(x^4)/y	y^{\prime\:}=\frac{x^{4}}{y}
y^'-1/2 y=2cos(x)	y^{\prime\:}-\frac{1}{2}y=2\cos(x)
límite cuando x tiende a 1 de 4/(2x-2)	\lim\:_{x\to\:1}(\frac{4}{2x-2})
(\partial)/(\partial x)(6x^2y^2+5x+8y^3)	\frac{\partial\:}{\partial\:x}(6x^{2}y^{2}+5x+8y^{3})
integral de (6x^3-5)/x	\int\:\frac{6x^{3}-5}{x}dx
límite cuando x tiende a 1 de (x^{15}-1)/(x^5-1)	\lim\:_{x\to\:1}(\frac{x^{15}-1}{x^{5}-1})

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