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Popular Calculus Problems

limit as x approaches 4 of (x^2-5)/(x+5)	\lim\:_{x\to\:4}(\frac{x^{2}-5}{x+5})
tangent of f(x)=3x^2-ln(x),(1,3)	tangent\:f(x)=3x^{2}-\ln(x),(1,3)
tangent of f(x)=x^5,\at x=4	tangent\:f(x)=x^{5},\at\:x=4
integral of (x^2+1)cos(2x)	\int\:(x^{2}+1)\cos(2x)dx
integral of sin(2x)e^{cos(2x)}	\int\:\sin(2x)e^{\cos(2x)}dx
integral of 7x^2+3+6/(x^2+1)	\int\:7x^{2}+3+\frac{6}{x^{2}+1}dx
derivative of (16/((5-x)^2)-1)	\frac{d}{dx}(\frac{16}{(5-x)^{2}}-1)
(pi/2)^'	(\frac{π}{2})^{\prime\:}
integral from 0 to 4 of 16-x^2	\int\:_{0}^{4}16-x^{2}dx
derivative of 3x^e+2e^x	derivative\:3x^{e}+2e^{x}
integral of (x+1)/(x(x-2)(x+3))	\int\:\frac{x+1}{x(x-2)(x+3)}dx
derivative of 6x(x^2-1)^2	derivative\:6x(x^{2}-1)^{2}
integral of x^30.2^{-x}x	\int\:x^{3}0.2^{-x}xdx
limit as x approaches+(-2) of 8/x	\lim\:_{x\to\:+(-2)}(\frac{8}{x})
taylor 9xln(1+2x)	taylor\:9x\ln(1+2x)
derivative of ln(x+y^2)	\frac{d}{dx}(\ln(x+y^{2}))
x(dy)/(dx)=y^2-y,y(1/4)= 1/4	x\frac{dy}{dx}=y^{2}-y,y(\frac{1}{4})=\frac{1}{4}
(\partial)/(\partial x)((e^x)/(y+x^7))	\frac{\partial\:}{\partial\:x}(\frac{e^{x}}{y+x^{7}})
tangent of 4x^3-18x^2-48x	tangent\:4x^{3}-18x^{2}-48x
derivative of 4-2x	\frac{d}{dx}(4-2x)
derivative of arcsec(x+2)	\frac{d}{dx}(\arcsec(x+2))
limit as x approaches infinity of 1/(-x)	\lim\:_{x\to\:\infty\:}(\frac{1}{-x})
integral of (2x^3-2/3 x^2+5x)	\int\:(2x^{3}-\frac{2}{3}x^{2}+5x)dx
integral of 1/(sqrt(x^2+20x))	\int\:\frac{1}{\sqrt{x^{2}+20x}}dx
(\partial)/(\partial x)(2x-sqrt(3y^2+z^2))	\frac{\partial\:}{\partial\:x}(2x-\sqrt{3y^{2}+z^{2}})
derivative of (14/(x^3))	\frac{d}{dx}(\frac{14}{x^{3}})
(\partial)/(\partial x)(x^{x/y}cos(x/y))	\frac{\partial\:}{\partial\:x}(x^{\frac{x}{y}}\cos(\frac{x}{y}))
sum from n=1 to infinity of 1/((5n-4)^4)	\sum\:_{n=1}^{\infty\:}\frac{1}{(5n-4)^{4}}
integral of-0.4x^2+1000	\int\:-0.4x^{2}+1000dx
(\partial}{\partial x}(ln(\frac{y^2)/x))	\frac{\partial\:}{\partial\:x}(\ln(\frac{y^{2}}{x}))
derivative of (x-4)^3+3x(x-4)^2	derivative\:(x-4)^{3}+3x(x-4)^{2}
limit as x approaches-infinity of x^6	\lim\:_{x\to\:-\infty\:}(x^{6})
(\partial)/(\partial x)(-4cos(3x))	\frac{\partial\:}{\partial\:x}(-4\cos(3x))
integral of (12s+12)/((s^2+1)(s-1)^3)	\int\:\frac{12s+12}{(s^{2}+1)(s-1)^{3}}ds
integral of 1/(4-x^2)	\int\:\frac{1}{4-x^{2}}dx
(dy)/(dx)=(-(3y)/(3x+2y))	\frac{dy}{dx}=(-\frac{3y}{3x+2y})
-6y^{''}+24y=0	-6y^{\prime\:\prime\:}+24y=0
(\partial)/(\partial y)(xye^{xz})	\frac{\partial\:}{\partial\:y}(xye^{xz})
limit as x approaches-infinity of x^2+2x	\lim\:_{x\to\:-\infty\:}(x^{2}+2x)
derivative of-(15x^4/2+(6x^2)/5-x/3-4)	\frac{d}{dx}(-\frac{15x^{4}}{2}+\frac{6x^{2}}{5}-\frac{x}{3}-4)
integral of xcos^3(x)	\int\:x\cos^{3}(x)dx
limit as x approaches 0 of (ln(1+1/x))/x	\lim\:_{x\to\:0}(\frac{\ln(1+\frac{1}{x})}{x})
derivative of x/((1-2x^2))	\frac{d}{dx}(\frac{x}{(1-2x)^{2}})
integral of (cos(x))^5sin(x)	\int\:(\cos(x))^{5}\sin(x)dx
integral of (x^2+2x)^5(2x+2)	\int\:(x^{2}+2x)^{5}(2x+2)dx
derivative of x^5e^{-x}	\frac{d}{dx}(x^{5}e^{-x})
derivative of (3x+5/(x^2-x))	\frac{d}{dx}(\frac{3x+5}{x^{2}-x})
integral from 0 to 3 of xsqrt(16-x^2)	\int\:_{0}^{3}x\sqrt{16-x^{2}}dx
limit as x approaches 0 of-xln(x)-x	\lim\:_{x\to\:0}(-x\ln(x)-x)
integral of x*sqrt(x)	\int\:x\cdot\:\sqrt{x}dx
derivative of 1/(x-1)	derivative\:\frac{1}{x-1}
x*y^'=sqrt(x^2-2xy-y^2)+y	x\cdot\:y^{\prime\:}=\sqrt{x^{2}-2xy-y^{2}}+y
integral of 3xsqrt(2x^2+1)	\int\:3x\sqrt{2x^{2}+1}dx
(\partial)/(\partial y)(4ze^{xyz})	\frac{\partial\:}{\partial\:y}(4ze^{xyz})
limit as x approaches-9-of (-6x)/(x+9)	\lim\:_{x\to\:-9-}(\frac{-6x}{x+9})
derivative of (x+3/(x^2+3))	\frac{d}{dx}(\frac{x+3}{x^{2}+3})
(dy)/(dx)=-y^2	\frac{dy}{dx}=-y^{2}
derivative of-5csc(x+sec(x))	\frac{d}{dx}(-5\csc(x)+\sec(x))
derivative of-(12/((x+2)^2))	\frac{d}{dx}(-\frac{12}{(x+2)^{2}})
derivative of 2/((x+2)^3)	derivative\:\frac{2}{(x+2)^{3}}
derivative of f(x)=6^x	derivative\:f(x)=6^{x}
(\partial)/(\partial y)(x^3+y^3-3xy)	\frac{\partial\:}{\partial\:y}(x^{3}+y^{3}-3xy)
area f(x)=4-3x,g(x)=2x^2-x	area\:f(x)=4-3x,g(x)=2x^{2}-x
integral from-3 to-2 of x^2e^{x^3+27}	\int\:_{-3}^{-2}x^{2}e^{x^{3}+27}dx
limit as x approaches 2 of 2x-9	\lim\:_{x\to\:2}(2x-9)
(\partial)/(\partial x)(-(xy)/((1+x)^3))	\frac{\partial\:}{\partial\:x}(-\frac{xy}{(1+x)^{3}})
tangent of y=sqrt(x)(1.1)	tangent\:y=\sqrt{x}(1.1)
derivative of x^3-8	\frac{d}{dx}(x^{3}-8)
limit as x approaches 0 of ((x-1)^3+1)/x	\lim\:_{x\to\:0}(\frac{(x-1)^{3}+1}{x})
integral from 0 to 8 of e^{x/2}	\int\:_{0}^{8}e^{\frac{x}{2}}dx
(\partial)/(\partial x)(x^3)	\frac{\partial\:}{\partial\:x}(x^{3})
y^'+10y=20	y^{\prime\:}+10y=20
sum from n=1 to infinity of n+(7/8)^n	\sum\:_{n=1}^{\infty\:}n+(\frac{7}{8})^{n}
tangent of y=x^3-x^2+x-1,(1,0)	tangent\:y=x^{3}-x^{2}+x-1,(1,0)
integral of x^4ln^2(x)	\int\:x^{4}\ln^{2}(x)dx
derivative of (4x/(x+4))	\frac{d}{dx}(\frac{4x}{x+4})
tangent of y=8+5x^2-2x^3	tangent\:y=8+5x^{2}-2x^{3}
inverse oflaplace (4s)/((s+2)^2)	inverselaplace\:\frac{4s}{(s+2)^{2}}
d/(dy)(x/y)	\frac{d}{dy}(\frac{x}{y})
integral from 0 to pi/(12) of tan(6x)	\int\:_{0}^{\frac{π}{12}}\tan(6x)dx
derivative of (x+6)/(x^3+x-7)	derivative\:\frac{x+6}{x^{3}+x-7}
integral of x(x+4)^6	\int\:x(x+4)^{6}dx
integral from 0 to 1 of cos^2(x)	\int\:_{0}^{1}\cos^{2}(x)dx
derivative of ln(6x+1)	\frac{d}{dx}(\ln(6x+1))
f(x)=x^2sqrt(2x+4)	f(x)=x^{2}\sqrt{2x+4}
integral of \sqrt[3]{tan(2x)}sec^2(2x)	\int\:\sqrt[3]{\tan(2x)}\sec^{2}(2x)dx
x^2(dy)/(dx)+xy=3	x^{2}\frac{dy}{dx}+xy=3
derivative of 1/((3+x^2))	\frac{d}{dx}(\frac{1}{(3+x)^{2}})
integral of e^{6x+7}	\int\:e^{6x+7}dx
tangent of 3/(1+x^2)	tangent\:\frac{3}{1+x^{2}}
tangent of xy-picos(y)=3pi,(2,pi)	tangent\:xy-π\cos(y)=3π,(2,π)
(\partial}{\partial t}(\frac{2r+s)/t)	\frac{\partial\:}{\partial\:t}(\frac{2r+s}{t})
derivative of-12sin(6x)	\frac{d}{dx}(-12\sin(6x))
derivative of y=(3x+4)^2	derivative\:y=(3x+4)^{2}
limit as x approaches 0 of (x^2+5)/(3^x)	\lim\:_{x\to\:0}(\frac{x^{2}+5}{3^{x}})
sum from n=1 to infinity of (-1)^n2^{-n}	\sum\:_{n=1}^{\infty\:}(-1)^{n}2^{-n}
(\partial)/(\partial x)(sin(x^2))	\frac{\partial\:}{\partial\:x}(\sin(x^{2}))
derivative of ln(1/(xsqrt(x+1)))	\frac{d}{dx}(\ln(\frac{1}{x\sqrt{x+1}}))
derivative of arccos(1/x)	\frac{d}{dx}(\arccos(\frac{1}{x}))
limit as x approaches 3-of (6x)/(x-3)	\lim\:_{x\to\:3-}(\frac{6x}{x-3})

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