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Popular Calculus Problems

y^'=20sqrt(x)y	y^{\prime\:}=20\sqrt{x}y
derivative of x/(sqrt(x-6))	\frac{d}{dx}(\frac{x}{\sqrt{x-6}})
integral of 1/4 x^2	\int\:\frac{1}{4}x^{2}dx
laplacetransform 6e^{-5t}+5t	laplacetransform\:6e^{-5t}+5t
derivative of y=(3x^4+9)/(x^2)	derivative\:y=\frac{3x^{4}+9}{x^{2}}
integral of (ln(x+1))^2	\int\:(\ln(x+1))^{2}dx
derivative of 2e^{2x}cos(x-e^{2x}sin(x))	\frac{d}{dx}(2e^{2x}\cos(x)-e^{2x}\sin(x))
integral of cot^4(5x)	\int\:\cot^{4}(5x)dx
derivative of f(x)=((x+8)/(x-8))^5	derivative\:f(x)=(\frac{x+8}{x-8})^{5}
integral of (-e^{1/x})/(x^2)	\int\:\frac{-e^{\frac{1}{x}}}{x^{2}}dx
integral of (x-y)	\int\:(x-y)dx
derivative of 5(sin(x^2)+2x^2cos(x^2))	derivative\:5(\sin(x^{2})+2x^{2}\cos(x^{2}))
integral of \sqrt[8]{cot(x)}csc^2(x)	\int\:\sqrt[8]{\cot(x)}\csc^{2}(x)dx
integral of 1/(a^2u^2)	\int\:\frac{1}{a^{2}u^{2}}du
(dy)/(dx)=xe^{x^2-y}	\frac{dy}{dx}=xe^{x^{2}-y}
derivative of y=-(e^{-x})/2 cos(2x)	derivative\:y=-\frac{e^{-x}}{2}\cos(2x)
derivative of e^{4x}cos(3x)	\frac{d}{dx}(e^{4x}\cos(3x))
integral of sin(4x)cos(4x)	\int\:\sin(4x)\cos(4x)dx
derivative of y=6e^x+2/(\sqrt[3]{x)}	derivative\:y=6e^{x}+\frac{2}{\sqrt[3]{x}}
integral of 3/(2x^2-4x+10)	\int\:\frac{3}{2x^{2}-4x+10}dx
derivative of x^3sqrt(5-x^2)	\frac{d}{dx}(x^{3}\sqrt{5-x^{2}})
implicit (dy)/(dx),x^2+y^2=25	implicit\:\frac{dy}{dx},x^{2}+y^{2}=25
(dx)/(dt)=4xt^5	\frac{dx}{dt}=4xt^{5}
derivative of (x+2)/(x^3+x-6)	derivative\:\frac{x+2}{x^{3}+x-6}
limit as x approaches 14 of sqrt(x+2)	\lim\:_{x\to\:14}(\sqrt{x+2})
derivative of g(x)=ln(xe^{-9x})	derivative\:g(x)=\ln(xe^{-9x})
area 4x+12,x^2	area\:4x+12,x^{2}
integral of sech(4x)tanh(4x)	\int\:\sech(4x)\tanh(4x)dx
area 5cos(7x),5-5cos(7x)	area\:5\cos(7x),5-5\cos(7x)
derivative of 6e^{2x}	\frac{d}{dx}(6e^{2x})
limit as x approaches 8 of f(x)	\lim\:_{x\to\:8}(f(x))
integral of 1/(x^2+x-2)	\int\:\frac{1}{x^{2}+x-2}dx
integral of sin(1-2x)	\int\:\sin(1-2x)dx
limit as x approaches-2 of (2x^2)/(2x+2)	\lim\:_{x\to\:-2}(\frac{2x^{2}}{2x+2})
slope ofintercept (0.5)(7.9)	slopeintercept\:(0.5)(7.9)
integral of 9e^{5x+e^{5x}}	\int\:9e^{5x+e^{5x}}dx
integral of x(4x-1)^4	\int\:x(4x-1)^{4}dx
derivative of y=ln(8x)	derivative\:y=\ln(8x)
y^{''}-7y^'=5t	y^{\prime\:\prime\:}-7y^{\prime\:}=5t
limit as x approaches 0 of x/(sin(4x))	\lim\:_{x\to\:0}(\frac{x}{\sin(4x)})
laplacetransform sin(t-pi)	laplacetransform\:\sin(t-π)
tangent of f(x)=x^2,\at x=0.2	tangent\:f(x)=x^{2},\at\:x=0.2
derivative of f(x)= 7/(x^2)	derivative\:f(x)=\frac{7}{x^{2}}
derivative of-1/(x^2+1)	\frac{d}{dx}(-\frac{1}{x^{2}}+1)
integral of 2sin(3x)cos(3x)	\int\:2\sin(3x)\cos(3x)dx
integral of (x^2)arctan(7x)	\int\:(x^{2})\arctan(7x)dx
integral of 2x^2ln(x)	\int\:2x^{2}\ln(x)dx
derivative of cos((1-e^{3x}/(1+e^{3x)}))	\frac{d}{dx}(\cos(\frac{1-e^{3x}}{1+e^{3x}}))
integral from 0 to 4 of sqrt(16-x^2)	\int\:_{0}^{4}\sqrt{16-x^{2}}dx
derivative of 1/(x^{19)}	derivative\:\frac{1}{x^{19}}
integral from-1 to 4 of 3x^2+8x-5	\int\:_{-1}^{4}3x^{2}+8x-5dx
integral of (7-5x)/(sqrt(64-49x^2))	\int\:\frac{7-5x}{\sqrt{64-49x^{2}}}dx
limit as t approaches 0 of (1-cos(t))/t	\lim\:_{t\to\:0}(\frac{1-\cos(t)}{t})
derivative of 4cos(x/2)	\frac{d}{dx}(4\cos(\frac{x}{2}))
y^{''}-3y=0	y^{\prime\:\prime\:}-3y=0
sum from n=0 to infinity of (x-10)^n	\sum\:_{n=0}^{\infty\:}(x-10)^{n}
derivative of (14)/(ln(x))	derivative\:\frac{14}{\ln(x)}
integral of θcsc^2(θ)	\int\:θ\csc^{2}(θ)dθ
[x-yarctan(y/x)]dx+xarctan(y/x)dy=0	[x-y\arctan(\frac{y}{x})]dx+x\arctan(\frac{y}{x})dy=0
limit as x approaches infinity of (e^{2x-7})/(6x)	\lim\:_{x\to\:\infty\:}(\frac{e^{2x-7}}{6x})
integral of (x^2-7)/(7x)	\int\:\frac{x^{2}-7}{7x}dx
derivative of 7e^xsqrt(x)	derivative\:7e^{x}\sqrt{x}
limit as x approaches infinity of 25-2x	\lim\:_{x\to\:\infty\:}(25-2x)
integral of 4/(xln(9x))	\int\:\frac{4}{x\ln(9x)}dx
integral of (3x^2-2x)	\int\:(3x^{2}-2x)dx
integral of cos(2kx)	\int\:\cos(2kx)dx
derivative of 2-4x^2	\frac{d}{dx}(2-4x^{2})
derivative of f(x)=(arccot(x))^5	derivative\:f(x)=(\arccot(x))^{5}
derivative of f(x)=(1-5x)/(4+x)	derivative\:f(x)=\frac{1-5x}{4+x}
derivative of e^{-x}*ln(x)	\frac{d}{dx}(e^{-x}\cdot\:\ln(x))
limit as x approaches 0 of b+0^c*ln(0)	\lim\:_{x\to\:0}(b+0^{c}\cdot\:\ln(0))
limit as k approaches infinity of 2k+1	\lim\:_{k\to\:\infty\:}(2k+1)
integral from 0 to 4 of (16-x^2)	\int\:_{0}^{4}(16-x^{2})dx
tangent of f(x)=4e^xcos(x),\at x=0	tangent\:f(x)=4e^{x}\cos(x),\at\:x=0
derivative of y=(5x^2+4)/(x+3)	derivative\:y=\frac{5x^{2}+4}{x+3}
integral of (sqrt(tan(x)+1))/(cos^2(x))	\int\:\frac{\sqrt{\tan(x)+1}}{\cos^{2}(x)}dx
integral of (3x^2)/(sqrt(x^3+8))	\int\:\frac{3x^{2}}{\sqrt{x^{3}+8}}dx
integral of (-8cos(-2))d	\int\:(-8\cos(-2))ddd
integral of 3cos(sqrt(7x))	\int\:3\cos(\sqrt{7x})dx
(\partial)/(\partial x)(3x^2-2xy+y^2-8y)	\frac{\partial\:}{\partial\:x}(3x^{2}-2xy+y^{2}-8y)
laplacetransform t+1	laplacetransform\:t+1
derivative of f(x)=(3-2x)/(3+2x)	derivative\:f(x)=\frac{3-2x}{3+2x}
derivative of {f}(x({g}(x)))	\frac{d}{dx}({f}(x)({g}(x)))
integral of (4x+5)^3	\int\:(4x+5)^{3}dx
derivative of 7x^{1/2}+x^{3/2}	\frac{d}{dx}(7x^{\frac{1}{2}}+x^{\frac{3}{2}})
sum from n=1 to infinity of arctan(2n)	\sum\:_{n=1}^{\infty\:}\arctan(2n)
integral of 5/(sqrt(x^2+16))	\int\:\frac{5}{\sqrt{x^{2}+16}}dx
integral from-4 to 6 of (x/2+6)	\int\:_{-4}^{6}(\frac{x}{2}+6)dx
(\partial)/(\partial x)(x+2y+3z)	\frac{\partial\:}{\partial\:x}(x+2y+3z)
integral from 0 to 0.6 of 10000x	\int\:_{0}^{0.6}10000xdx
derivative of 9x^3	derivative\:9x^{3}
d/(dt)((3t^2)/(sqrt(1+4t^2+9t^4)))	\frac{d}{dt}(\frac{3t^{2}}{\sqrt{1+4t^{2}+9t^{4}}})
integral of e^{x^2}x^3	\int\:e^{x^{2}}x^{3}dx
integral from 0 to 4 of 2pi(2-y)(4y^2)	\int\:_{0}^{4}2π(2-y)(4y^{2})dy
derivative of (e^x)/(e^x+1)	derivative\:\frac{e^{x}}{e^{x}+1}
y^{''}+5y=-180x^2e^{5x}	y^{\prime\:\prime\:}+5y=-180x^{2}e^{5x}
integral of sin(mx)	\int\:\sin(mx)dx
(dy)/(dx)=((y-x+1)/(y-x-6))	\frac{dy}{dx}=(\frac{y-x+1}{y-x-6})
limit as x approaches 0 of cos(7/x)	\lim\:_{x\to\:0}(\cos(\frac{7}{x}))
derivative of f(x)=-8x^2	derivative\:f(x)=-8x^{2}

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