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Popular Calculus Problems

derivative of x/((1-x^2))	\frac{d}{dx}(\frac{x}{(1-x)^{2}})
derivative of f(x)= 7/(r^3)	derivative\:f(x)=\frac{7}{r^{3}}
integral of (cos(x))/(1+7sin(x))	\int\:\frac{\cos(x)}{1+7\sin(x)}dx
integral of cos(x^4)	\int\:\cos(x^{4})dx
(y^{12}x)(dy)/(dx)=1+x	(y^{12}x)\frac{dy}{dx}=1+x
derivative of (-x^2/2)	\frac{d}{dx}(\frac{-x^{2}}{2})
derivative of f(x)=7x^{3/2}	derivative\:f(x)=7x^{\frac{3}{2}}
(\partial)/(\partial x)(cos(7x^2y-3xy^3))	\frac{\partial\:}{\partial\:x}(\cos(7x^{2}y-3xy^{3}))
integral of (e^{(a+1)x})/a	\int\:\frac{e^{(a+1)x}}{a}dx
area 4x,x^2,3	area\:4x,x^{2},3
derivative of cos(9x)	derivative\:\cos(9x)
derivative of y=(sqrt(x))/(x+3)	derivative\:y=\frac{\sqrt{x}}{x+3}
derivative of-ae^{-x}	\frac{d}{dx}(-ae^{-x})
(\partial ^2)/(\partial y^2)(x^2-e^{y^2})	\frac{\partial\:^{2}}{\partial\:y^{2}}(x^{2}-e^{y^{2}})
integral from 0 to pi/8 of xtan^2(2x)	\int\:_{0}^{\frac{π}{8}}x\tan^{2}(2x)dx
integral of 1/(4u^2+9-41u)	\int\:\frac{1}{4u^{2}+9-41u}du
laplacetransform-sin(2t)	laplacetransform\:-\sin(2t)
integral of 1/(5+4cos(x))	\int\:\frac{1}{5+4\cos(x)}dx
sum from n=6 to infinity of (5^n)/(14^n)	\sum\:_{n=6}^{\infty\:}\frac{5^{n}}{14^{n}}
derivative of (sqrt(x)/(x-10))	\frac{d}{dx}(\frac{\sqrt{x}}{x-10})
taylor ln(1-z)	taylor\:\ln(1-z)
integral of 3x^2-24x+48	\int\:3x^{2}-24x+48dx
integral of (x^2-7x-12)/(x(x^2+3x+3))	\int\:\frac{x^{2}-7x-12}{x(x^{2}+3x+3)}dx
derivative of 3x^4-8x^3+2	\frac{d}{dx}(3x^{4}-8x^{3}+2)
derivative of f(x)=-5x^2-6x+200	derivative\:f(x)=-5x^{2}-6x+200
derivative of log_{6}(x)	derivative\:\log_{6}(x)
y^{''}+2t=0	y^{\prime\:\prime\:}+2t=0
integral from-1 to 2 of-x^2+x+2	\int\:_{-1}^{2}-x^{2}+x+2dx
integral of 1/((x^2+36)^{3/2)}	\int\:\frac{1}{(x^{2}+36)^{\frac{3}{2}}}dx
(\partial)/(\partial y)((t^2+y^2)^{3/2})	\frac{\partial\:}{\partial\:y}((t^{2}+y^{2})^{\frac{3}{2}})
tangent of f(x)=(2x+4)^{1/5},\at x=1	tangent\:f(x)=(2x+4)^{\frac{1}{5}},\at\:x=1
limit as y approaches infinity of ((y^2-e^{(6y)}))/((4y^2+e^{7y))}	\lim\:_{y\to\:\infty\:}(\frac{(y^{2}-e^{(6y)})}{(4y^{2}+e^{7y})})
derivative of h(t)=(t+1)^{2/3}(2t^2-1)^3	derivative\:h(t)=(t+1)^{\frac{2}{3}}(2t^{2}-1)^{3}
(\partial)/(\partial y)(4x^3y^3+1)	\frac{\partial\:}{\partial\:y}(4x^{3}y^{3}+1)
sum from n=0 to infinity of 0.1^n	\sum\:_{n=0}^{\infty\:}0.1^{n}
integral of 1/(5x+6)	\int\:\frac{1}{5x+6}dx
36y^{''}-y=xe^{x/6}	36y^{\prime\:\prime\:}-y=xe^{\frac{x}{6}}
derivative of 3x+8	derivative\:3x+8
integral of (3x+6)/((2x^2+8x+3)^2)	\int\:\frac{3x+6}{(2x^{2}+8x+3)^{2}}dx
tangent of y= 8/(x-2),\at x=6	tangent\:y=\frac{8}{x-2},\at\:x=6
derivative of 26e^{x^2}x	\frac{d}{dx}(26e^{x^{2}}x)
(\partial)/(\partial y)(5xsin(y-z))	\frac{\partial\:}{\partial\:y}(5x\sin(y-z))
derivative of (7x^2-12xe^x)	\frac{d}{dx}((7x^{2}-12x)e^{x})
y^'-e^{5x+y}=0	y^{\prime\:}-e^{5x+y}=0
e^y+((xe^y+1)dy)/(dx)=0	e^{y}+\frac{(xe^{y}+1)dy}{dx}=0
derivative of (3x+2/(5x-1))	\frac{d}{dx}(\frac{3x+2}{5x-1})
limit as x approaches-4 of 2/((x+4)^3)	\lim\:_{x\to\:-4}(\frac{2}{(x+4)^{3}})
derivative of 6+3x-4x(7x+1^2)	\frac{d}{dx}(6+3x-4x(7x+1)^{2})
integral of 13ln(\sqrt[3]{x})	\int\:13\ln(\sqrt[3]{x})dx
integral of 6x^4-6x^3+4x^2+C	\int\:6x^{4}-6x^{3}+4x^{2}+Cdx
(\partial)/(\partial x)(2xyln(x))	\frac{\partial\:}{\partial\:x}(2xy\ln(x))
(\partial)/(\partial t)(sin(2x)cos(2t))	\frac{\partial\:}{\partial\:t}(\sin(2x)\cos(2t))
integral of (6x^2+2x-1)	\int\:(6x^{2}+2x-1)dx
inverse oflaplace ((2s+12))/(s^2+2s+5)	inverselaplace\:\frac{(2s+12)}{s^{2}+2s+5}
(\partial)/(\partial x)((x-6)(y+4))	\frac{\partial\:}{\partial\:x}((x-6)(y+4))
derivative of (8x/(7-tan(x)))	\frac{d}{dx}(\frac{8x}{7-\tan(x)})
(dy)/(dt)=-2ty+4e^{-t^2}	\frac{dy}{dt}=-2ty+4e^{-t^{2}}
derivative of x^{2/3}(5/2-x)	\frac{d}{dx}(x^{\frac{2}{3}}(\frac{5}{2}-x))
longdivision (2x+3)/(3x-2)	longdivision\:\frac{2x+3}{3x-2}
taylor sin(9x)sin(2x)	taylor\:\sin(9x)\sin(2x)
limit as x approaches infinity of 2(x)^2	\lim\:_{x\to\:\infty\:}(2(x)^{2})
integral of 5/(x^2-36)	\int\:\frac{5}{x^{2}-36}dx
(\partial)/(\partial t)(3t^2)	\frac{\partial\:}{\partial\:t}(3t^{2})
derivative of arctan(2x+3)	\frac{d}{dx}(\arctan(2x+3))
integral of (-9cos(x))	\int\:(-9\cos(x))dx
integral of x^2-9x+14	\int\:x^{2}-9x+14dx
integral of (x+2)/(x^2+5x)	\int\:\frac{x+2}{x^{2}+5x}dx
(dy)/(dx)=5x-y	\frac{dy}{dx}=5x-y
integral from 0 to 6 of 2e^x	\int\:_{0}^{6}2e^{x}dx
inverse oflaplace 1/(s(s+2)(s+3))	inverselaplace\:\frac{1}{s(s+2)(s+3)}
integral of x^4(x^5-2)^3	\int\:x^{4}(x^{5}-2)^{3}dx
derivative of sin(arccos(2x))	\frac{d}{dx}(\sin(\arccos(2x)))
derivative of 5cos(4ln(x))	\frac{d}{dx}(5\cos(4\ln(x)))
derivative of sqrt(8x)-sqrt(3x)	\frac{d}{dx}(\sqrt{8x}-\sqrt{3x})
integral from 0 to 30 of 9sqrt(x)	\int\:_{0}^{30}9\sqrt{x}dx
(\partial)/(\partial u)(v/u)	\frac{\partial\:}{\partial\:u}(\frac{v}{u})
integral from 0 to 3 of \|2x-4\|	\int\:_{0}^{3}\left\|2x-4\right\|dx
integral of (7x^6+x/7)	\int\:(7x^{6}+\frac{x}{7})dx
implicit (dy)/(dx),x^2=y^3	implicit\:\frac{dy}{dx},x^{2}=y^{3}
derivative of (arccos(x)^{10})	\frac{d}{dx}((\arccos(x))^{10})
derivative of (2-x^4)	\frac{d}{dx}((2-x)^{4})
integral of (sqrt(25+5x))/x	\int\:\frac{\sqrt{25+5x}}{x}dx
derivative of sin(x^3+sin^3(x))	\frac{d}{dx}(\sin(x^{3})+\sin^{3}(x))
integral from-4 to 1 of (3x+6)	\int\:_{-4}^{1}(3x+6)dx
derivative of (arctan(x)^3)	\frac{d}{dx}((\arctan(x))^{3})
(\partial)/(\partial x)(1/(f(x))-1/x)	\frac{\partial\:}{\partial\:x}(\frac{1}{f(x)}-\frac{1}{x})
(\partial)/(\partial z)((x+y)/(z-2y))	\frac{\partial\:}{\partial\:z}(\frac{x+y}{z-2y})
derivative of sqrt(y^2+x^2)	\frac{d}{dx}(\sqrt{y^{2}+x^{2}})
integral of sin(1/7)x	\int\:\sin(\frac{1}{7})xdx
limit as h approaches 0 of (((h-5)^2-25))/((h))	\lim\:_{h\to\:0}(\frac{((h-5)^{2}-25)}{(h)})
d/(dy)(2xy^3)	\frac{d}{dy}(2xy^{3})
integral of-1/s e^{-st}	\int\:-\frac{1}{s}e^{-st}dt
integral of x(4x+5)^8	\int\:x(4x+5)^{8}dx
limit as x approaches infinity of 5^{-1/x}	\lim\:_{x\to\:\infty\:}(5^{-\frac{1}{x}})
derivative of f(x)=x^7-x^3	derivative\:f(x)=x^{7}-x^{3}
derivative of y=sin(1/x)	derivative\:y=\sin(\frac{1}{x})
integral of sin^6(3x)cos(3x)	\int\:\sin^{6}(3x)\cos(3x)dx
integral of x^3(3+x^2)^5	\int\:x^{3}(3+x^{2})^{5}dx
integral from 1 to 4 of \|x^2-2x-15\|	\int\:_{1}^{4}\left\|x^{2}-2x-15\right\|dx
limit as x approaches 0 of 6/x	\lim\:_{x\to\:0}(\frac{6}{x})

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