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Popular Calculus Problems

limit as h approaches+0 of 2x+h	\lim\:_{h\to\:+0}(2x+h)
(\partial)/(\partial x)(ln(x^3+y^5))	\frac{\partial\:}{\partial\:x}(\ln(x^{3}+y^{5}))
(\partial)/(\partial y)((x+y)^2)	\frac{\partial\:}{\partial\:y}((x+y)^{2})
integral from 0 to 1 of 4x5^x	\int\:_{0}^{1}4x5^{x}dx
limit as x approaches-2 of 2x+4	\lim\:_{x\to\:-2}(2x+4)
derivative of 500x-0.003x^2+10^{-8}x^3	derivative\:500x-0.003x^{2}+10^{-8}x^{3}
derivative of 1/3*(x-5^3)	\frac{d}{dx}(\frac{1}{3}\cdot\:(x-5)^{3})
derivative of 2sin(x+5cos(3pix))	\frac{d}{dx}(2\sin(x)+5\cos(3πx))
derivative of (x^4+5x^2)	\frac{d}{dx}((x^{4}+5x)^{2})
derivative of log_{2}(x^2+1)-2^3	derivative\:\log_{2}(x^{2}+1)-2^{3}
integral of (3/x+x/3)	\int\:(\frac{3}{x}+\frac{x}{3})dx
derivative of ln(x/3)	\frac{d}{dx}(\ln(\frac{x}{3}))
(\partial)/(\partial z)(x^2ye^{y/z})	\frac{\partial\:}{\partial\:z}(x^{2}ye^{\frac{y}{z}})
integral of sin(x)sin(4x)	\int\:\sin(x)\sin(4x)dx
derivative of e^{x+7}	\frac{d}{dx}(e^{x+7})
(\partial)/(\partial x)(-(e^{y/x}y)/(x^2)+e^{-x}y)	\frac{\partial\:}{\partial\:x}(-\frac{e^{\frac{y}{x}}y}{x^{2}}+e^{-x}y)
sum from n=0 to infinity of e^{1/n}	\sum\:_{n=0}^{\infty\:}e^{\frac{1}{n}}
laplacetransform 2e^{-2t}cos(3t)	laplacetransform\:2e^{-2t}\cos(3t)
integral of 1/2 e^xsin(x)	\int\:\frac{1}{2}e^{x}\sin(x)dx
inverse oflaplace 1/(2002s^2+4)	inverselaplace\:\frac{1}{2002s^{2}+4}
integral of (2x)/(4+x^2)	\int\:\frac{2x}{4+x^{2}}dx
derivative of e^{cos(x+ln(x)})	\frac{d}{dx}(e^{\cos(x)+\ln(x)})
derivative of 3arcsin(x)	derivative\:3\arcsin(x)
integral of (x^4)/((6+x^5)^2)	\int\:\frac{x^{4}}{(6+x^{5})^{2}}dx
integral of 4tan^3(sin(x))cos(x)	\int\:4\tan^{3}(\sin(x))\cos(x)dx
integral of x\sqrt[3]{6x+7}	\int\:x\sqrt[3]{6x+7}dx
(d^2y)/(dx^2)+4(dy)/(dx)+5y=2e^{-2x}	\frac{d^{2}y}{dx^{2}}+4\frac{dy}{dx}+5y=2e^{-2x}
(dy)/(dt)=4y+y^4,y(0)=1	\frac{dy}{dt}=4y+y^{4},y(0)=1
derivative of (-24/(x^4))	\frac{d}{dx}(\frac{-24}{x^{4}})
integral of 2+ye^y	\int\:2+ye^{y}dy
limit as x approaches 0-of x/(sin(3x))	\lim\:_{x\to\:0-}(\frac{x}{\sin(3x)})
integral from-4 to 4 of xsqrt(16-x^2)	\int\:_{-4}^{4}x\sqrt{16-x^{2}}dx
tangent of g(x)= 1/(2sqrt(x)),\at x=9	tangent\:g(x)=\frac{1}{2\sqrt{x}},\at\:x=9
area x^{1/2},x-2,[0,4]	area\:x^{\frac{1}{2}},x-2,[0,4]
7x-4ysqrt(x^2+1)(dy)/(dx)=0,y(0)=6	7x-4y\sqrt{x^{2}+1}\frac{dy}{dx}=0,y(0)=6
taylor 7tan(x)	taylor\:7\tan(x)
derivative of ex^2-y	\frac{d}{dx}(ex^{2}-y)
integral of sqrt(x)sqrt(1-x)	\int\:\sqrt{x}\sqrt{1-x}dx
integral of (x^2+3)^52x	\int\:(x^{2}+3)^{5}2xdx
(\partial)/(\partial x)(-(x^2)/(y^2))	\frac{\partial\:}{\partial\:x}(-\frac{x^{2}}{y^{2}})
integral of 64e^{8x}sin(8x)	\int\:64e^{8x}\sin(8x)dx
integral of ((arcsin(x))^3)/(sqrt(1-x^2))	\int\:\frac{(\arcsin(x))^{3}}{\sqrt{1-x^{2}}}dx
(\partial)/(\partial x)(cos^2(x)+sin^2(y))	\frac{\partial\:}{\partial\:x}(\cos^{2}(x)+\sin^{2}(y))
integral of sin^2(t)an(t)	\int\:\sin^{2}(t)d\tan(t)
tangent of f(x)=37x-16x^2,\at x=1	tangent\:f(x)=37x-16x^{2},\at\:x=1
integral of (2sec^2(x))	\int\:(2\sec^{2}(x))dx
integral of 6/(x(x^2+4)^2)	\int\:\frac{6}{x(x^{2}+4)^{2}}dx
(d^2)/(dx^2)(e^xcos(x))	\frac{d^{2}}{dx^{2}}(e^{x}\cos(x))
x(dy)/(dx)+(1+x)y=(sin(2x))/(e^x)	x\frac{dy}{dx}+(1+x)y=\frac{\sin(2x)}{e^{x}}
(xdy)/(dx)+4y=x^3-x	\frac{xdy}{dx}+4y=x^{3}-x
(e^{3x}cos(2x))^'	(e^{3x}\cos(2x))^{\prime\:}
y^{''}-4y^'+4y=16-4t-6te^{2t}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=16-4t-6te^{2t}
limit as x approaches 5 of-4	\lim\:_{x\to\:5}(-4)
integral of x4^{x^2}	\int\:x4^{x^{2}}dx
d/(dt)(te^t)	\frac{d}{dt}(te^{t})
derivative of g(t)=(3t^2-1)/(2t+5)	derivative\:g(t)=\frac{3t^{2}-1}{2t+5}
integral of 33arctan(sqrt(x))	\int\:33\arctan(\sqrt{x})dx
limit as x approaches 0-of (e^{2/x}*sin(pi(x)))/(x+2)+x	\lim\:_{x\to\:0-}(\frac{e^{\frac{2}{x}}\cdot\:\sin(π(x))}{x+2}+x)
limit as x approaches 0 of (8sin(0))/0	\lim\:_{x\to\:0}(\frac{8\sin(0)}{0})
area x+y=3,y^2=4x,y=0,1	area\:x+y=3,y^{2}=4x,y=0,1
integral of (sin^2(x)+cos(x))^2	\int\:(\sin^{2}(x)+\cos(x))^{2}dx
tangent of f(x)=x-2sin(x)	tangent\:f(x)=x-2\sin(x)
integral from 0 to 2 of x/(x^4+1)	\int\:_{0}^{2}\frac{x}{x^{4}+1}dx
taylor e^{-x^2},0	taylor\:e^{-x^{2}},0
derivative of (x^4+1^{1/2})	\frac{d}{dx}((x^{4}+1)^{\frac{1}{2}})
integral of 2sqrt(z)	\int\:2\sqrt{z}dz
derivative of (7x-1)/(x^2+9x)	derivative\:\frac{7x-1}{x^{2}+9x}
integral from-11 to 0 of xsqrt(25-x)	\int\:_{-11}^{0}x\sqrt{25-x}dx
derivative of x^2+2xy+y^2	\frac{d}{dx}(x^{2}+2xy+y^{2})
(\partial)/(\partial x)(4sin(x))	\frac{\partial\:}{\partial\:x}(4\sin(x))
integral from-2 to 1 of (x+1)sqrt(x+3)	\int\:_{-2}^{1}(x+1)\sqrt{x+3}dx
derivative of x^3+2x-1	derivative\:x^{3}+2x-1
derivative of F(x)=7x^6(x^4-7x)	derivative\:F(x)=7x^{6}(x^{4}-7x)
derivative of tan(sqrt(3x))	\frac{d}{dx}(\tan(\sqrt{3x}))
tangent of f(x)=2x^2,\at x=4	tangent\:f(x)=2x^{2},\at\:x=4
integral of cos(pix)	\int\:\cos(πx)dx
(\partial)/(\partial y)(x^3-3xy^2)	\frac{\partial\:}{\partial\:y}(x^{3}-3xy^{2})
derivative of 1-(1-0.01t)^3	derivative\:1-(1-0.01t)^{3}
integral of (ln(x))/(x^8)	\int\:\frac{\ln(x)}{x^{8}}dx
integral from 0 to 1 of (33)/(4y-1)	\int\:_{0}^{1}\frac{33}{4y-1}dy
integral from 0 to infinity of 2	\int\:_{0}^{\infty\:}2dx
(\partial)/(\partial y)(x^2cos(xy))	\frac{\partial\:}{\partial\:y}(x^{2}\cos(xy))
derivative of f(x)=e^x\sqrt[3]{x}	derivative\:f(x)=e^{x}\sqrt[3]{x}
derivative of y=x^3-7x^2+8x+1	derivative\:y=x^{3}-7x^{2}+8x+1
integral of (arctan(e^x))/(e^x)	\int\:\frac{\arctan(e^{x})}{e^{x}}dx
integral of 4/(4-t^2)	\int\:\frac{4}{4-t^{2}}dt
limit as x approaches 1 of (x+4)/(1+x^2)	\lim\:_{x\to\:1}(\frac{x+4}{1+x^{2}})
integral of xsqrt(x^2+4)	\int\:x\sqrt{x^{2}+4}dx
limit as x approaches 0 of ((a^x-b^x))/x	\lim\:_{x\to\:0}(\frac{(a^{x}-b^{x})}{x})
integral of (70)/(49-x^2)	\int\:\frac{70}{49-x^{2}}dx
tangent of f(x)x^2+3ay,x=-1	tangent\:f(x)x^{2}+3ay,x=-1
area 5x-x^2,x	area\:5x-x^{2},x
(\partial)/(\partial x)(x^4y^5+3x^9y)	\frac{\partial\:}{\partial\:x}(x^{4}y^{5}+3x^{9}y)
integral of (3x+4y)	\int\:(3x+4y)dx
d/(du)(v/(u-v))	\frac{d}{du}(\frac{v}{u-v})
integral from 0 to 2 of x^2+2	\int\:_{0}^{2}x^{2}+2dx
integral of (-4ln^2(x))/x	\int\:\frac{-4\ln^{2}(x)}{x}dx
(\partial)/(\partial x)((xy^2)/(x^2+y^4))	\frac{\partial\:}{\partial\:x}(\frac{xy^{2}}{x^{2}+y^{4}})
(\partial)/(\partial v)(2sin(u)sin(v))	\frac{\partial\:}{\partial\:v}(2\sin(u)\sin(v))
derivative of (5x/(x+2))	\frac{d}{dx}(\frac{5x}{x+2})

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