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Problemas populares de Cálculo

y^'=sqrt(x^9+1)	y^{\prime\:}=\sqrt{x^{9}+1}
derivative h(t)=t^2(7t+8)^3	derivative\:h(t)=t^{2}(7t+8)^{3}
(d^2)/(dx^2)(7sec(x))	\frac{d^{2}}{dx^{2}}(7\sec(x))
(\partial)/(\partial x)(((2+t^2))/(3x-x^3))	\frac{\partial\:}{\partial\:x}(\frac{(2+t^{2})}{3x-x^{3}})
derivative y=e^{2-x}	derivative\:y=e^{2-x}
integral de 0 a 3 de (sqrt(9-x^2))	\int\:_{0}^{3}(\sqrt{9-x^{2}})dx
d/(da)((tan^2(a)-sin^2(a))/(tan^2(a)))	\frac{d}{da}(\frac{\tan^{2}(a)-\sin^{2}(a)}{\tan^{2}(a)})
derivada de 8xy-1/4 (x+y^4)	\frac{d}{dx}(8xy-\frac{1}{4}(x+y)^{4})
f(x)=x^2cos(x^2)	f(x)=x^{2}\cos(x^{2})
implicit (dy)/(dx),y=-x	implicit\:\frac{dy}{dx},y=-x
integral de (ln(x^3))/x	\int\:\frac{\ln(x^{3})}{x}dx
límite cuando x tiende a 2 de (2-\|x\|)/(2+x)	\lim\:_{x\to\:2}(\frac{2-\left\|x\right\|}{2+x})
integral de-pi/3 a 0 de 3sec^3(x)	\int\:_{-\frac{π}{3}}^{0}3\sec^{3}(x)dx
límite cuando x tiende a 7-de (4-3x)/(x-7)	\lim\:_{x\to\:7-}(\frac{4-3x}{x-7})
integral de (x+5)^2	\int\:(x+5)^{2}dx
derivada de arctan(x/(sqrt(1-x^2)))	\frac{d}{dx}(\arctan(\frac{x}{\sqrt{1-x^{2}}}))
(dx)/(dt)+1/t x=t^3x^4	\frac{dx}{dt}+\frac{1}{t}x=t^{3}x^{4}
(\partial)/(\partial x)((4x)/(3y))	\frac{\partial\:}{\partial\:x}(\frac{4x}{3y})
integral de (6x^2+x+25)/((x+1)(x^2+4))	\int\:\frac{6x^{2}+x+25}{(x+1)(x^{2}+4)}dx
derivative (x^3-9)sqrt(x)	derivative\:(x^{3}-9)\sqrt{x}
derivative (2w^3-w)/w	derivative\:\frac{2w^{3}-w}{w}
integral de t(t^2+1)^5	\int\:t(t^{2}+1)^{5}dt
serie de n=0 a infinity de (n-1)/(n^2)	\sum\:_{n=0}^{\infty\:}\frac{n-1}{n^{2}}
integral de 1+e^t	\int\:1+e^{t}dt
y^{''}+0.1y^'+0.0004y=0	y^{\prime\:\prime\:}+0.1y^{\prime\:}+0.0004y=0
tangent f(x)=(x-6)/(x+2),\at x=2	tangent\:f(x)=\frac{x-6}{x+2},\at\:x=2
derivative sqrt(8)x-sqrt(3x)	derivative\:\sqrt{8}x-\sqrt{3x}
(1/2-3/2*10/9+4)^'	(\frac{1}{2}-\frac{3}{2}\cdot\:\frac{10}{9}+4)^{\prime\:}
6(x^2+y^2)dx+7xydy=0	6(x^{2}+y^{2})dx+7xydy=0
derivada de 6x^2e^x	\frac{d}{dx}(6x^{2}e^{x})
área sqrt(x-2),(x-4)^2,x=5	area\:\sqrt{x-2},(x-4)^{2},x=5
derivada de cos(x/3 cos(x))	\frac{d}{dx}(\cos(\frac{x}{3})\cos(x))
integral de e^{x^2}*2x	\int\:e^{x^{2}}\cdot\:2xdx
integral de 1/(2-3x)	\int\:\frac{1}{2-3x}dx
límite cuando x tiende a 0 de ((1+x)^6-1)/x	\lim\:_{x\to\:0}(\frac{(1+x)^{6}-1}{x})
xy^'-y=x^2e^x	xy^{\prime\:}-y=x^{2}e^{x}
(\partial)/(\partial x)(-5xy^4-2ycos(x))	\frac{\partial\:}{\partial\:x}(-5xy^{4}-2y\cos(x))
maclaurin cos(x)	maclaurin\:\cos(x)
derivada de x^2*3y	\frac{d}{dx}(x^{2}\cdot\:3y)
integral de sqrt(4r^2+1)	\int\:\sqrt{4r^{2}+1}dr
integral de-1/2 a 0 de (1/2+2y+3z)	\int\:_{-\frac{1}{2}}^{0}(\frac{1}{2}+2y+3z)dy
(\partial)/(\partial x)(e^{xsin(y)})	\frac{\partial\:}{\partial\:x}(e^{x\sin(y)})
taylor sqrt(1+2x)	taylor\:\sqrt{1+2x}
límite cuando x tiende a 2 de (3x+4)/(8x-1)	\lim\:_{x\to\:2}(\frac{3x+4}{8x-1})
integral de 1/(usqrt(3-u^2))	\int\:\frac{1}{u\sqrt{3-u^{2}}}du
integral de xx'	\int\:xx\prime\:dx
inversalaplace (400)/(s(s^2+200))	inverselaplace\:\frac{400}{s(s^{2}+200)}
límite cuando x tiende a infinity de 3^{-x}	\lim\:_{x\to\:\infty\:}(3^{-x})
derivada de (x-1(ln(x)))	\frac{d}{dx}((x-1)(\ln(x)))
(\partial)/(\partial x)(3sin(4x))	\frac{\partial\:}{\partial\:x}(3\sin(4x))
derivada de-(x^4/4)	\frac{d}{dx}(-\frac{x^{4}}{4})
(dy)/(y^3)=x^{-2}dx	\frac{dy}{y^{3}}=x^{-2}dx
integral de (3^x)/(1+9^x)	\int\:\frac{3^{x}}{1+9^{x}}dx
derivative-(12)/(x^5)	derivative\:-\frac{12}{x^{5}}
tangent f(x)=-3x^2-4x	tangent\:f(x)=-3x^{2}-4x
d/(dy)((1-cos(y))/(1-cos(2y)))	\frac{d}{dy}(\frac{1-\cos(y)}{1-\cos(2y)})
derivative (150t)/(t+3)	derivative\:\frac{150t}{t+3}
integral de tsqrt(9t^2+4)	\int\:t\sqrt{9t^{2}+4}dt
área x^2,x^4-3x^2,-2,2	area\:x^{2},x^{4}-3x^{2},-2,2
límite cuando x tiende a a de x^{sin(x)}	\lim\:_{x\to\:a}(x^{\sin(x)})
partialfraction (x^2)/(2x+4)	partialfraction\:\frac{x^{2}}{2x+4}
(dx)/(dt)-2x=x^3	\frac{dx}{dt}-2x=x^{3}
derivada de ln(x-2x^2)	\frac{d}{dx}(\ln(x)-2x^{2})
derivada de (5x/(sqrt(x^2+1)))	\frac{d}{dx}(\frac{5x}{\sqrt{x^{2}+1}})
derivative e^{yx^2}	derivative\:e^{yx^{2}}
derivada de (3x-4^2)	\frac{d}{dx}((3x-4)^{2})
derivada de x(12-2x^2)	\frac{d}{dx}(x(12-2x)^{2})
integral de 8e^{4x}cos(6x)	\int\:8e^{4x}\cos(6x)dx
y^{''}+2y^'+2y=sin(7x)	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(7x)
(\partial)/(\partial x)(e^{-x^3-y^6})	\frac{\partial\:}{\partial\:x}(e^{-x^{3}-y^{6}})
derivada de-sqrt(x^2+y^2)-10	\frac{d}{dx}(-\sqrt{x^{2}+y^{2}}-10)
integral de sin^3(x)cos(y)	\int\:\sin^{3}(x)\cos(y)dx
integral de 1/(1+u)	\int\:\frac{1}{1+u}du
derivative y=xln(x)cos(x)	derivative\:y=x\ln(x)\cos(x)
integral de (3x^3+5x)/(x^2-x-2)	\int\:\frac{3x^{3}+5x}{x^{2}-x-2}dx
límite cuando x tiende a-infinity de arccos(x)	\lim\:_{x\to\:-\infty\:}(\arccos(x))
integral de (x^2-15L)/(x+7)	\int\:\frac{x^{2}-15L}{x+7}dx
integral de (x^2)/((1-25x^2)^{3/2)}	\int\:\frac{x^{2}}{(1-25x^{2})^{\frac{3}{2}}}dx
derivative (1-3x-x^2)/(x^2-3)	derivative\:\frac{1-3x-x^{2}}{x^{2}-3}
laplacetransformación 2t^3	laplacetransform\:2t^{3}
derivada de sin(xln(x^2+1))	\frac{d}{dx}(\sin(x)\ln(x^{2}+1))
implicit (dy)/(dx),tan(x-y)= y/(1-x^2)	implicit\:\frac{dy}{dx},\tan(x-y)=\frac{y}{1-x^{2}}
integral de cot(42x)	\int\:\cot(42x)dx
integral de (x^3+3x)/((x^2+1)^2)	\int\:\frac{x^{3}+3x}{(x^{2}+1)^{2}}dx
derivada de 3^{sqrt(x^3-x+1)}	\frac{d}{dx}(3^{\sqrt{x^{3}-x+1}})
derivada de arcsec(x/a)	\frac{d}{dx}(\arcsec(\frac{x}{a}))
integral de-infinity a 0 de 1/(5-8x)	\int\:_{-\infty\:}^{0}\frac{1}{5-8x}dx
derivada de x^2sec(1/(x^3))	\frac{d}{dx}(x^{2}\sec(\frac{1}{x^{3}}))
integral de (x^3)/(x^8+5)	\int\:\frac{x^{3}}{x^{8}+5}dx
(\partial)/(\partial x)(e^{2y}(3e^y-2x))	\frac{\partial\:}{\partial\:x}(e^{2y}(3e^{y}-2x))
inversalaplace (s+1)/((s+6)^2*(s+2))	inverselaplace\:\frac{s+1}{(s+6)^{2}\cdot\:(s+2)}
derivada de-e^{x-28}+75	\frac{d}{dx}(-e^{x-28}+75)
integral de-x-2	\int\:-x-2dx
derivative f(x)=2xe^x+(x^2-14)*e^x	derivative\:f(x)=2xe^{x}+(x^{2}-14)\cdot\:e^{x}
límite cuando x tiende a-2 de 1/(x^2-4)	\lim\:_{x\to\:-2}(\frac{1}{x^{2}-4})
integral de (1/(x^2)-1/(x^3))	\int\:(\frac{1}{x^{2}}-\frac{1}{x^{3}})dx
derivada de (x^5/(5-x^4))	\frac{d}{dx}(\frac{x^{5}}{5-x^{4}})
laplacetransformación-2	laplacetransform\:-2
derivada de ln(x^2-8x)	\frac{d}{dx}(\ln(x^{2}-8x))
límite cuando x tiende a pi de cos(tan(x))	\lim\:_{x\to\:π}(\cos(\tan(x)))

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