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Popular Calculus Problems

maclaurin 10^x	maclaurin\:10^{x}
(dy)/(dx)-5y=6e^{8x}	\frac{dy}{dx}-5y=6e^{8x}
derivative of e^{1/(x^2}+1/(e^{x^2)})	\frac{d}{dx}(e^{\frac{1}{x^{2}}}+\frac{1}{e^{x^{2}}})
integral of sqrt((x^2)/4-4x+17)	\int\:\sqrt{\frac{x^{2}}{4}-4x+17}dx
derivative of in(x+3)	\frac{d}{dx}(in(x+3))
((x^2+2y^2)dx)/(dy)=xy	\frac{(x^{2}+2y^{2})dx}{dy}=xy
integral from 5 to 8 of y/(y^2-y-2)	\int\:_{5}^{8}\frac{y}{y^{2}-y-2}dy
area e^x,e^{5x},0,1	area\:e^{x},e^{5x},0,1
derivative of f(x)=\sqrt[7]{x}-7e^x	derivative\:f(x)=\sqrt[7]{x}-7e^{x}
derivative of 1-sin(2x)	\frac{d}{dx}(1-\sin(2x))
(\partial)/(\partial x)(z^3ln(yx))	\frac{\partial\:}{\partial\:x}(z^{3}\ln(yx))
laplacetransform 2((t-1)^2)1((t-1))	laplacetransform\:2\cdot\:((t-1)^{2})\cdot\:1((t-1))
(\partial)/(\partial x)((7x)/(3y))	\frac{\partial\:}{\partial\:x}(\frac{7x}{3y})
normal of f(x)= x/(2x-3),(1,-1)	normal\:f(x)=\frac{x}{2x-3},(1,-1)
integral of (e^{-st})/(s^2)	\int\:\frac{e^{-st}}{s^{2}}dt
derivative of y=(100)/(x^4)	derivative\:y=\frac{100}{x^{4}}
f(x)=14400+600x+x^2	f(x)=14400+600x+x^{2}
(\partial)/(\partial x)(sin(2x)cos(y))	\frac{\partial\:}{\partial\:x}(\sin(2x)\cos(y))
(dy)/(dx)=e^{6x}+8y	\frac{dy}{dx}=e^{6x}+8y
(dy)/(dx)=5x(x-4)	\frac{dy}{dx}=5x(x-4)
integral of (\sqrt[7]{x})	\int\:(\sqrt[7]{x})dx
integral of 15x	\int\:15xdx
tangent of g(x)=e^{x^5-6x},\at x=-1	tangent\:g(x)=e^{x^{5}-6x},\at\:x=-1
derivative of (2x^2+6x+8)/(sqrt(x))	derivative\:\frac{2x^{2}+6x+8}{\sqrt{x}}
integral of (sqrt(u))/2	\int\:\frac{\sqrt{u}}{2}du
(\partial)/(\partial x)(x^2sin(y)cos(y))	\frac{\partial\:}{\partial\:x}(x^{2}\sin(y)\cos(y))
d/(dv)(u^2-v^2)	\frac{d}{dv}(u^{2}-v^{2})
integral from 0 to 2 of 1/(x+2)	\int\:_{0}^{2}\frac{1}{x+2}dx
limit as x approaches 0 of ((cos(11x)-cos(6x)))/x	\lim\:_{x\to\:0}(\frac{(\cos(11x)-\cos(6x))}{x})
derivative of f(x)=x^3sin(x)	derivative\:f(x)=x^{3}\sin(x)
derivative of (x^2-6x+1/((x^2-1)^2))	\frac{d}{dx}(\frac{x^{2}-6x+1}{(x^{2}-1)^{2}})
integral of cos(x)(5+5sin^2(x))	\int\:\cos(x)(5+5\sin^{2}(x))dx
integral from 0 to 1 of (\sqrt[3]{1+7x})	\int\:_{0}^{1}(\sqrt[3]{1+7x})dx
integral of x^2-9x+3	\int\:x^{2}-9x+3dx
tangent of f(x)=xsqrt(x),(9,27)	tangent\:f(x)=x\sqrt{x},(9,27)
sum from n=1 to infinity of 9/(6+9^n)	\sum\:_{n=1}^{\infty\:}\frac{9}{6+9^{n}}
limit as x approaches-3 of (x^2-5)/(3-x)	\lim\:_{x\to\:-3}(\frac{x^{2}-5}{3-x})
integral of 1/(1-9x^2)	\int\:\frac{1}{1-9x^{2}}dx
integral of 2cos(x^2)	\int\:2\cos(x^{2})dx
derivative of (2x^2+8x+8/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}+8x+8}{\sqrt{x}})
derivative of f(x)=(2e^x-3x^5)	derivative\:f(x)=(2e^{x}-3x^{5})
integral of 1/(4t^2-4t+5)	\int\:\frac{1}{4t^{2}-4t+5}dt
(\partial)/(\partial x)(-4y^3sin(4x))	\frac{\partial\:}{\partial\:x}(-4y^{3}\sin(4x))
derivative of sin(x-csc(x))	\frac{d}{dx}(\sin(x)-\csc(x))
integral of (2x^2-3)^2	\int\:(2x^{2}-3)^{2}dx
limit as x approaches 2 of sqrt(x/(x-2))	\lim\:_{x\to\:2}(\sqrt{\frac{x}{x-2}})
limit as x approaches infinity of x^3	\lim\:_{x\to\:\infty\:}(x^{3})
derivative of cos(x)+isin(x)	derivative\:\cos(x)+i\sin(x)
integral of e^{2x}x	\int\:e^{2x}xdx
integral of 9x^2-24x-36	\int\:9x^{2}-24x-36dx
derivative of cos(1-4x)	\frac{d}{dx}(\cos(1-4x))
derivative of f(x)=(3-(1/(x^2)))/(x+4)	derivative\:f(x)=\frac{3-(\frac{1}{x^{2}})}{x+4}
integral of e^{-st}cos(t)	\int\:e^{-st}\cos(t)dt
ty^'=2	ty^{\prime\:}=2
derivative of sec^2(sqrt(x))	\frac{d}{dx}(\sec^{2}(\sqrt{x}))
derivative of (sin(x)/(8xe^x))	\frac{d}{dx}(\frac{\sin(x)}{8xe^{x}})
d/(dt)(t^5)	\frac{d}{dt}(t^{5})
limit as x approaches 0 of tan(x)ln(x)	\lim\:_{x\to\:0}(\tan(x)\ln(x))
tangent of 1/(x^5)	tangent\:\frac{1}{x^{5}}
integral of (x+1)(2x^2+sqrt(x))	\int\:(x+1)(2x^{2}+\sqrt{x})dx
(d^2y)/(dx^2)+6(dy)/(dx)=0	\frac{d^{2}y}{dx^{2}}+6\frac{dy}{dx}=0
limit as x approaches-3 of (3-\|x\|)/(3+x)	\lim\:_{x\to\:-3}(\frac{3-\left\|x\right\|}{3+x})
y^{''}+6y^'+34y=25e^{-3x}	y^{\prime\:\prime\:}+6y^{\prime\:}+34y=25e^{-3x}
derivative of 4x-5x^{5/6}	\frac{d}{dx}(4x-5x^{\frac{5}{6}})
derivative of f(x)=xcos(x)+2tan(x)	derivative\:f(x)=x\cos(x)+2\tan(x)
integral of coth(x/3)	\int\:\coth(\frac{x}{3})dx
derivative of a*e^x	\frac{d}{dx}(a\cdot\:e^{x})
limit as x approaches-5-of 2/(x^2-25)	\lim\:_{x\to\:-5-}(\frac{2}{x^{2}-25})
sum from n=1 to infinity of (6n)/(8n+9)	\sum\:_{n=1}^{\infty\:}\frac{6n}{8n+9}
integral of p^8ln(p)	\int\:p^{8}\ln(p)dp
integral of cos^3(8x)sin^{-2}(8x)	\int\:\cos^{3}(8x)\sin^{-2}(8x)dx
y^'=((y^2+1))/(2y)	y^{\prime\:}=\frac{(y^{2}+1)}{2y}
integral of (12x^2+x+2)/(x(x^2+1))	\int\:\frac{12x^{2}+x+2}{x(x^{2}+1)}dx
sum from n=1 to infinity of 3/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{3}{n+1}
derivative of f(x)=sin(8x+4)	derivative\:f(x)=\sin(8x+4)
integral of (48x^2)/((x-21)(x+7)^2)	\int\:\frac{48x^{2}}{(x-21)(x+7)^{2}}dx
derivative of 4x+4	\frac{d}{dx}(4x+4)
derivative of 1/(x(x+2^2))	\frac{d}{dx}(\frac{1}{x(x+2)^{2}})
(tan(2x))^'	(\tan(2x))^{\prime\:}
((4x^3)/3+2x+cos(x)+1)^'	(\frac{4x^{3}}{3}+2x+\cos(x)+1)^{\prime\:}
integral of (sqrt(16-4x^2))	\int\:(\sqrt{16-4x^{2}})dx
derivative of 2-sin(x)	\frac{d}{dx}(2-\sin(x))
(x^2-x)(dy)/(dx)=y-2xy	(x^{2}-x)\frac{dy}{dx}=y-2xy
integral from 0 to 2 of 7x^3sqrt(x^2+4)	\int\:_{0}^{2}7x^{3}\sqrt{x^{2}+4}dx
derivative of (x^2+6x/(10-x^2))	\frac{d}{dx}(\frac{x^{2}+6x}{10-x^{2}})
y^{''}-7y^'+10y=-sin(3t)	y^{\prime\:\prime\:}-7y^{\prime\:}+10y=-\sin(3t)
area y=x^2+2x-11,y=3,[3,5]	area\:y=x^{2}+2x-11,y=3,[3,5]
(\partial)/(\partial x)(4xsin(7x^2y))	\frac{\partial\:}{\partial\:x}(4x\sin(7x^{2}y))
tangent of f(x)=3x^2-5x	tangent\:f(x)=3x^{2}-5x
tangent of f(x)=-4/3 x^{-5/2},\at x=4	tangent\:f(x)=-\frac{4}{3}x^{-\frac{5}{2}},\at\:x=4
derivative of x(x-1(x-2))	\frac{d}{dx}(x(x-1)(x-2))
derivative of y=\sqrt[7]{x}	derivative\:y=\sqrt[7]{x}
area-4x^2+9,x+7	area\:-4x^{2}+9,x+7
y^'+5y=te^{(4t)}	y^{\prime\:}+5y=te^{(4t)}
(\partial)/(\partial x)(3x^2-4)	\frac{\partial\:}{\partial\:x}(3x^{2}-4)
integral of 9/(9+e^x)	\int\:\frac{9}{9+e^{x}}dx
integral of (-1)/(2sqrt(16-x))	\int\:\frac{-1}{2\sqrt{16-x}}dx
limit as x approaches infinity of ce^x	\lim\:_{x\to\:\infty\:}(ce^{x})
derivative of 4x^2+8	\frac{d}{dx}(4x^{2}+8)
integral from 0 to pi of cos(x)-sin(x)	\int\:_{0}^{π}\cos(x)-\sin(x)dx

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