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Popular Calculus Problems

derivative of f(x)= 2/(2x+1)	derivative\:f(x)=\frac{2}{2x+1}
derivative of (2z^3)/3-z	derivative\:\frac{2z^{3}}{3}-z
derivative of f(t)=e^{2tsin(2t)}	derivative\:f(t)=e^{2t\sin(2t)}
integral from 0 to 1 of x(1-x)^{10}	\int\:_{0}^{1}x(1-x)^{10}dx
yy^'-21e^x=0	yy^{\prime\:}-21e^{x}=0
sum from n=1 to infinity of 1/(6^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{6^{n}}
(\partial)/(\partial x)((2x)/(x^2+7y))	\frac{\partial\:}{\partial\:x}(\frac{2x}{x^{2}+7y})
derivative of (1-t)(1+t^2)^{-1}	derivative\:(1-t)(1+t^{2})^{-1}
integral from 1 to e^2 of 1/x	\int\:_{1}^{e^{2}}\frac{1}{x}dx
slope ofintercept (2,-3),(4,-2)	slopeintercept\:(2,-3),(4,-2)
derivative of f(x)=(ln(x))/(x^4)	derivative\:f(x)=\frac{\ln(x)}{x^{4}}
limit as x approaches 1-of 2	\lim\:_{x\to\:1-}(2)
(\partial)/(\partial y)(ln(x-9y))	\frac{\partial\:}{\partial\:y}(\ln(x-9y))
y^'+3y=9-e^t	y^{\prime\:}+3y=9-e^{t}
area y=\|x-9\|,y= x/2	area\:y=\left\|x-9\right\|,y=\frac{x}{2}
laplacetransform x^2cos(x)	laplacetransform\:x^{2}\cos(x)
cos(y)((dy)/(dt))+sin(y)=0	\cos(y)(\frac{dy}{dt})+\sin(y)=0
integral from-3 to x^3 of t^3	\int\:_{-3}^{x^{3}}t^{3}dt
limit as x approaches-2 of x^2+9x+6	\lim\:_{x\to\:-2}(x^{2}+9x+6)
integral of ((5-e^x))/(e^{2x)}	\int\:\frac{(5-e^{x})}{e^{2x}}dx
f(x)=xarccos(x)	f(x)=x\arccos(x)
(\partial)/(\partial x)(A(B-x^2-y^2-z^2))	\frac{\partial\:}{\partial\:x}(A(B-x^{2}-y^{2}-z^{2}))
derivative of f(x)=(5x^6+4x^3)^4	derivative\:f(x)=(5x^{6}+4x^{3})^{4}
derivative of x+2x^2sin(1/x)	\frac{d}{dx}(x+2x^{2}\sin(\frac{1}{x}))
derivative of y=-2x^2+4x-4	derivative\:y=-2x^{2}+4x-4
limit as x approaches-infinity of ln(x)	\lim\:_{x\to\:-\infty\:}(\ln(x))
derivative of f(x)=(x^2)/(5+8x)	derivative\:f(x)=\frac{x^{2}}{5+8x}
y^{''}+2y^'=1+t^2+e^{-2t}	y^{\prime\:\prime\:}+2y^{\prime\:}=1+t^{2}+e^{-2t}
(d^2y)/(dx^2)+4y=sin(2x)	\frac{d^{2}y}{dx^{2}}+4y=\sin(2x)
derivative of (-x/y)	\frac{d}{dx}(\frac{-x}{y})
tangent of 2/(sqrt(x+5))	tangent\:\frac{2}{\sqrt{x+5}}
slope of (-1,-4),(5,-4)	slope\:(-1,-4),(5,-4)
derivative of 4x-5x^{7/8}	\frac{d}{dx}(4x-5x^{\frac{7}{8}})
tangent of f(x)=8e^x+x,(0,8)	tangent\:f(x)=8e^{x}+x,(0,8)
integral from 1 to e^2 of (ln^3(x^2))/x	\int\:_{1}^{e^{2}}\frac{\ln^{3}(x^{2})}{x}dx
sum from n=0 to infinity of (n!)/(10^n)	\sum\:_{n=0}^{\infty\:}\frac{n!}{10^{n}}
(dy)/(dx)=y(8x^2+6)	\frac{dy}{dx}=y(8x^{2}+6)
integral from e to infinity of (ln(x))/x	\int\:_{e}^{\infty\:}\frac{\ln(x)}{x}dx
tangent of f(x)=(8x)/(x^2+1)	tangent\:f(x)=\frac{8x}{x^{2}+1}
(4-t^2)y^'+2ty=3t^2	(4-t^{2})y^{\prime\:}+2ty=3t^{2}
integral of 1/2 t^2	\int\:\frac{1}{2}t^{2}dt
(\partial)/(\partial x)(xe^y+ye^{-x})	\frac{\partial\:}{\partial\:x}(xe^{y}+ye^{-x})
integral of (5x+7y)	\int\:(5x+7y)dx
area f(x)=2sin(x)+x,-pi,pi	area\:f(x)=2\sin(x)+x,-π,π
(2/((1-x)^3))^'	(\frac{2}{(1-x)^{3}})^{\prime\:}
(\partial)/(\partial y)(cos(2y))	\frac{\partial\:}{\partial\:y}(\cos(2y))
integral from 1 to e of x^3*ln(x)	\int\:_{1}^{e}x^{3}\cdot\:\ln(x)dx
(1-x^2)(dy)/(dx)=2y	(1-x^{2})\frac{dy}{dx}=2y
ye^{-x}(dy)/(dx)=x	ye^{-x}\frac{dy}{dx}=x
(\partial)/(\partial z)(xy+z^3x-2yz)	\frac{\partial\:}{\partial\:z}(xy+z^{3}x-2yz)
integral of 18cos^2(89x)	\int\:18\cos^{2}(89x)dx
derivative of arctan(sqrt(t))	derivative\:\arctan(\sqrt{t})
integral of (16x+7)	\int\:(16x+7)dx
derivative of (x^{2/3}(x-4))	\frac{d}{dx}((x^{\frac{2}{3}})(x-4))
integral of (9x-16)^3	\int\:(9x-16)^{3}dx
derivative of ln((3x+4/(3x-4)))	\frac{d}{dx}(\ln(\frac{3x+4}{3x-4}))
integral of sin(t)2t	\int\:\sin(t)2tdt
integral of (sin(2x))/(e^x)	\int\:\frac{\sin(2x)}{e^{x}}dx
derivative of (4e^x/(2e^x+1))	\frac{d}{dx}(\frac{4e^{x}}{2e^{x}+1})
laplacetransform sqrt(2)sin(sqrt(2)t)	laplacetransform\:\sqrt{2}\sin(\sqrt{2}t)
(dy}{dx}y=\frac{x^3)/3-x	\frac{dy}{dx}y=\frac{x^{3}}{3}-x
(\partial)/(\partial x)(cos^6(x^8y^9))	\frac{\partial\:}{\partial\:x}(\cos^{6}(x^{8}y^{9}))
y^{''}+5y^'+4y=0	y^{\prime\:\prime\:}+5y^{\prime\:}+4y=0
integral of (10)/(x^2)	\int\:\frac{10}{x^{2}}dx
(\partial)/(\partial x)(7e^xcos(yz))	\frac{\partial\:}{\partial\:x}(7e^{x}\cos(yz))
derivative of x^4f(x)	derivative\:x^{4}f(x)
((dy)/(dx))-3y=e^{2x}	(\frac{dy}{dx})-3y=e^{2x}
y^{''}+4y^'=6e^{-3t}	y^{\prime\:\prime\:}+4y^{\prime\:}=6e^{-3t}
(dy)/(dx)+(9y)/(1000+x)=0.405	\frac{dy}{dx}+\frac{9y}{1000+x}=0.405
tangent of f(x)=3sin(x),\at x= pi/4	tangent\:f(x)=3\sin(x),\at\:x=\frac{π}{4}
tangent of f(x)=x^2-4x+3,\at x=1	tangent\:f(x)=x^{2}-4x+3,\at\:x=1
integral of (15arctan(x))/(x^2)	\int\:\frac{15\arctan(x)}{x^{2}}dx
integral from x^2 to 1 of ln(2t^2+1)	\int\:_{x^{2}}^{1}\ln(2t^{2}+1)dt
sum from n=5 to infinity of e^{3-2n}	\sum\:_{n=5}^{\infty\:}e^{3-2n}
integral of 3t^2sin(2t^3+1)	\int\:3t^{2}\sin(2t^{3}+1)dt
integral of (2x)/x	\int\:\frac{2x}{x}dx
sum from n=1 to infinity of (17n!)/(n^n)	\sum\:_{n=1}^{\infty\:}\frac{17n!}{n^{n}}
area y^2=4x,y=0,y=4	area\:y^{2}=4x,y=0,y=4
(3x^2+y+3x^3y)dx+(x)dy=0	(3x^{2}+y+3x^{3}y)dx+(x)dy=0
integral of 1/(sqrt(1-(x+1)^2))	\int\:\frac{1}{\sqrt{1-(x+1)^{2}}}dx
(\partial)/(\partial y)(ln(x^2+y^2+z^2))	\frac{\partial\:}{\partial\:y}(\ln(x^{2}+y^{2}+z^{2}))
integral of ((y-1)(y-5))/(y^3-y^2+3y+5)	\int\:\frac{(y-1)(y-5)}{y^{3}-y^{2}+3y+5}dy
integral of 2+sqrt(6x)	\int\:2+\sqrt{6x}dx
sum from n=1 to infinity of x^{n+1}	\sum\:_{n=1}^{\infty\:}x^{n+1}
(\partial)/(\partial x)(xe^{xy})	\frac{\partial\:}{\partial\:x}(x\cdot\:e^{x\cdot\:y})
integral of 5/(sqrt(4-(2x)^2))	\int\:\frac{5}{\sqrt{4-(2x)^{2}}}dx
integral from 2 to 3 of 1/(sqrt(x-3))	\int\:_{2}^{3}\frac{1}{\sqrt{x-3}}dx
derivative of y=3x^2-4	derivative\:y=3x^{2}-4
integral of 1+cos(4x)	\int\:1+\cos(4x)dx
derivative of 5x^3+4x	derivative\:5x^{3}+4x
integral from 0 to infinity of 1/(x^2+x)	\int\:_{0}^{\infty\:}\frac{1}{x^{2}+x}dx
(\partial)/(\partial y)(1/(x^2+y^2+1))	\frac{\partial\:}{\partial\:y}(\frac{1}{x^{2}+y^{2}+1})
(dy)/(dx)=-0.05y	\frac{dy}{dx}=-0.05y
(\partial)/(\partial y)(2xy^4-4)	\frac{\partial\:}{\partial\:y}(2xy^{4}-4)
integral of x^3(x^2+1)^8	\int\:x^{3}(x^{2}+1)^{8}dx
d/(d{z)}({x}e^{({y})/({z)}})	\frac{d}{d{z}}({x}e^{\frac{{y}}{{z}}})
integral of 1/((ax+b)^4)	\int\:\frac{1}{(ax+b)^{4}}dx
integral from 0 to 1 of pi(y^2-y^4)	\int\:_{0}^{1}π(y^{2}-y^{4})dy
(\partial)/(\partial x)(z^2+5x^2+y^2)	\frac{\partial\:}{\partial\:x}(z^{2}+5x^{2}+y^{2})
integral of 3x^2-4x	\int\:3x^{2}-4xdx

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