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Popular Calculus Problems

derivative of D(X^9)	derivative\:D(X^{9})
7yy^'cos^2(x)=sin(x)(sqrt(3y^2-pi))	7yy^{\prime\:}\cos^{2}(x)=\sin(x)(\sqrt{3y^{2}-π})
(\partial)/(\partial x)(3x^4y^2+3)	\frac{\partial\:}{\partial\:x}(3x^{4}y^{2}+3)
integral of e^xsqrt(64-e^{2x)}	\int\:e^{x}\sqrt{64-e^{2x}}dx
limit as x approaches 0 of (e^x-2^x)/x	\lim\:_{x\to\:0}(\frac{e^{x}-2^{x}}{x})
tangent of f(x)=ln(4-x^2+2x^4),\at x=1	tangent\:f(x)=\ln(4-x^{2}+2x^{4}),\at\:x=1
laplacetransform f(t)= 9/4 t^2e^{2t}e^{3t}	laplacetransform\:f(t)=\frac{9}{4}t^{2}\cdot\:e^{2t}\cdot\:e^{3t}
integral of 128cos^4(8x)	\int\:128\cos^{4}(8x)dx
integral of y^2sqrt(y)	\int\:y^{2}\sqrt{y}dy
derivative of (8x^2+2x+6/(sqrt(x)))	\frac{d}{dx}(\frac{8x^{2}+2x+6}{\sqrt{x}})
integral from 2 to 5 of x^3	\int\:_{2}^{5}x^{3}dx
integral of (u^5-3u^4-u^2+2/7)	\int\:(u^{5}-3u^{4}-u^{2}+\frac{2}{7})du
derivative of-3/x	derivative\:-\frac{3}{x}
derivative of 2xsin(x+cos(x)x^2)	\frac{d}{dx}(2x\sin(x)+\cos(x)x^{2})
limit as x approaches infinity of 3*x	\lim\:_{x\to\:\infty\:}(3\cdot\:x)
integral of (17)/(xln(3x))	\int\:\frac{17}{x\ln(3x)}dx
derivative of 2-x^2	\frac{d}{dx}(2-x^{2})
tangent of 4x(3-2x)^5,\at x=2	tangent\:4x(3-2x)^{5},\at\:x=2
integral of (sqrt(x^2-a^2))/(x^4)	\int\:\frac{\sqrt{x^{2}-a^{2}}}{x^{4}}dx
(2x)^'	(2x)^{\prime\:}
integral of ((cos^3(x)))/3	\int\:\frac{(\cos^{3}(x))}{3}dx
limit as x approaches 3 of (2x^2-4x-8)^6	\lim\:_{x\to\:3}((2x^{2}-4x-8)^{6})
(\partial}{\partial x}(\frac{4x)/y)	\frac{\partial\:}{\partial\:x}(\frac{4x}{y})
integral of (4x-2)/(x^3-x^2-2x)	\int\:\frac{4x-2}{x^{3}-x^{2}-2x}dx
derivative of y=sin(t^3)	derivative\:y=\sin(t^{3})
integral from 0 to N of e^{-st}e^{3t}	\int\:_{0}^{N}e^{-st}e^{3t}dt
integral of 2/3 x^2	\int\:\frac{2}{3}x^{2}dx
integral of (x^3+3)/(x^2)	\int\:\frac{x^{3}+3}{x^{2}}dx
y^'+4y=3sin(e^4x)	y^{\prime\:}+4y=3\sin(e^{4}x)
integral of x^m	\int\:x^{m}dx
integral of 1/(x^4+4x^2)	\int\:\frac{1}{x^{4}+4x^{2}}dx
y^{''}+2y^'+5y=4e^{-t}cos(2t)	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=4e^{-t}\cos(2t)
xdx-y^2dy=0	x\cdot\:dx-y^{2}\cdot\:dy=0
y^'=x^2+1	y^{\prime\:}=x^{2}+1
integral of t/((t^2+1)^{15/2)}	\int\:\frac{t}{(t^{2}+1)^{\frac{15}{2}}}dt
integral of (x^6-2x^3)^5(x^5-x^2)	\int\:(x^{6}-2x^{3})^{5}(x^{5}-x^{2})dx
derivative of 1/(\sqrt[3]{(8-x^3)^8)}	derivative\:\frac{1}{\sqrt[3]{(8-x^{3})^{8}}}
area x=y^2-4y,x=-y^2+4y	area\:x=y^{2}-4y,x=-y^{2}+4y
tangent of y=x^2-x,(4,12)	tangent\:y=x^{2}-x,(4,12)
integral of 1/(x^2(x+1)^3)	\int\:\frac{1}{x^{2}(x+1)^{3}}dx
derivative of f(x)=(5x)/(x-3)	derivative\:f(x)=\frac{5x}{x-3}
sum from n=1 to infinity of (2)^{n-1}	\sum\:_{n=1}^{\infty\:}(2)^{n-1}
1/(sqrt(x^2+1))((dy)/(dx))=xe^y	\frac{1}{\sqrt{x^{2}+1}}(\frac{dy}{dx})=xe^{y}
integral of 4/(x^2-1)	\int\:\frac{4}{x^{2}-1}dx
derivative of-1/2 sin(x)	\frac{d}{dx}(-\frac{1}{2}\sin(x))
integral of (x^2)/(sqrt(a^2-x^2))	\int\:\frac{x^{2}}{\sqrt{a^{2}-x^{2}}}dx
area e^x,e^{-x},[-1,1]	area\:e^{x},e^{-x},[-1,1]
integral of 1/((x^2-121)^{3/2)}	\int\:\frac{1}{(x^{2}-121)^{\frac{3}{2}}}dx
derivative of 8x^6+5w^2+7w	derivative\:8x^{6}+5w^{2}+7w
tangent of y=3x^2+10x+2,\at x=1	tangent\:y=3x^{2}+10x+2,\at\:x=1
limit as x approaches infinity of 2^{2x}	\lim\:_{x\to\:\infty\:}(2^{2x})
derivative of y=(3x-1)/(6x+5)	derivative\:y=\frac{3x-1}{6x+5}
(1/2 arcsin(x)+1/4 sin(2arcsin(x)))^'	(\frac{1}{2}\arcsin(x)+\frac{1}{4}\sin(2\arcsin(x)))^{\prime\:}
derivative of xg(x)f(x)	derivative\:x\cdot\:g(x)\cdot\:f(x)
derivative of f(x)=(6x^2-x+7)^{-5/3}	derivative\:f(x)=(6x^{2}-x+7)^{-\frac{5}{3}}
(dy)/(dt)=k(y-60)	\frac{dy}{dt}=k(y-60)
integral of x/((4x+5)^2)	\int\:\frac{x}{(4x+5)^{2}}dx
limit as x approaches 1 of (x^3+2)(3-x)	\lim\:_{x\to\:1}((x^{3}+2)(3-x))
limit as x approaches 3 of ((4x^2+3x))/5	\lim\:_{x\to\:3}(\frac{(4x^{2}+3x)}{5})
inverse oflaplace (10)/(2s+10)	inverselaplace\:\frac{10}{2s+10}
integral of (cos(1/x))/(x^2)	\int\:\frac{\cos(\frac{1}{x})}{x^{2}}dx
derivative of (log_{10}(n))^2	derivative\:(\log_{10}(n))^{2}
xy^'-y= 3/2 xln(x)	xy^{\prime\:}-y=\frac{3}{2}x\ln(x)
integral of (5x-1)/(x^2-3x-40)	\int\:\frac{5x-1}{x^{2}-3x-40}dx
tangent of f(x)= x/(8-x),\at x=3	tangent\:f(x)=\frac{x}{8-x},\at\:x=3
(\partial)/(\partial x)(2xe^{x/2+y}+2)	\frac{\partial\:}{\partial\:x}(2xe^{\frac{x}{2}+y}+2)
integral of 1/((6+sqrt(x))^3)	\int\:\frac{1}{(6+\sqrt{x})^{3}}dx
derivative of 7(\sqrt[3]{x}+(x^{1/3})/3)	derivative\:7(\sqrt[3]{x}+\frac{x^{\frac{1}{3}}}{3})
tangent of f(x)= 1/(1+x^2),(-1, 1/2)	tangent\:f(x)=\frac{1}{1+x^{2}},(-1,\frac{1}{2})
f(x)=(sin(x))/(2x)	f(x)=\frac{\sin(x)}{2x}
integral from-pi to pi of sin(x)sin(nx)	\int\:_{-π}^{π}\sin(x)\sin(nx)dx
taylor 1/(3+5x)	taylor\:\frac{1}{3+5x}
derivative of y=x^{5/2}e^x	derivative\:y=x^{\frac{5}{2}}e^{x}
f(x)=(ln(x))/(2x)	f(x)=\frac{\ln(x)}{2x}
integral of x^5sqrt(x^3+6)	\int\:x^{5}\sqrt{x^{3}+6}dx
(\partial)/(\partial x)(yz-xw)	\frac{\partial\:}{\partial\:x}(yz-xw)
derivative of \sqrt[3]{x+7}	\frac{d}{dx}(\sqrt[3]{x+7})
xy^{''}+5y^'=0	xy^{\prime\:\prime\:}+5y^{\prime\:}=0
(\partial)/(\partial y)(5xy^3)	\frac{\partial\:}{\partial\:y}(5xy^{3})
tangent of y=x^2+5x+2,(-5,2)	tangent\:y=x^{2}+5x+2,(-5,2)
tangent of f(x)=-3-6x^2,(-2,27)	tangent\:f(x)=-3-6x^{2},(-2,27)
f(t)=tsin(t)	f(t)=t\sin(t)
derivative of tan((x^2/(2x+3)))	\frac{d}{dx}(\tan(\frac{x^{2}}{2x+3}))
integral of-csc(x)	\int\:-\csc(x)dx
(\partial)/(\partial x)(ln(y)+2xy^3)	\frac{\partial\:}{\partial\:x}(\ln(y)+2xy^{3})
y^{''}+9y=3xe^{2x}	y^{\prime\:\prime\:}+9y=3xe^{2x}
limit as t approaches 0 of (e^{5t}-1)/t	\lim\:_{t\to\:0}(\frac{e^{5t}-1}{t})
integral of f^{-1}(x)	\int\:f^{-1}(x)dx
derivative of 4cos((2pi)/3)	derivative\:4\cos(\frac{2π}{3})
derivative of cos(a^3+x^3)	derivative\:\cos(a^{3}+x^{3})
derivative of f(x(5x^2-4))	\frac{d}{dx}(f(x)(5x^{2}-4))
integral of (8e^{-1/x})/(x^2)	\int\:\frac{8e^{-\frac{1}{x}}}{x^{2}}dx
derivative of-6/((1-x)^4)	derivative\:-\frac{6}{(1-x)^{4}}
(d^2)/(dx^2)((-6-7t)^6)	\frac{d^{2}}{dx^{2}}((-6-7t)^{6})
integral from 1 to 4 of sqrt(t)	\int\:_{1}^{4}\sqrt{t}dt
y^'=e^{y+2x}	y^{\prime\:}=e^{y+2x}
integral from 0 to 1 of ((3t^2)/(1+t^3))	\int\:_{0}^{1}(\frac{3t^{2}}{1+t^{3}})dt
integral of 1/(6+x)	\int\:\frac{1}{6+x}dx
integral of sqrt(9+x^2)	\int\:\sqrt{9+x^{2}}dx
(sec(x^5+x))^'	(\sec(x^{5}+x))^{\prime\:}

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