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Popular Calculus Problems

derivative of (5x)/(e^x)	derivative\:\frac{5x}{e^{x}}
x^2y^{''}-4xy^'=x^5	x^{2}y^{\prime\:\prime\:}-4xy^{\prime\:}=x^{5}
derivative of f(x)=(3x^2-x+5)(x^2+3x-9)	derivative\:f(x)=(3x^{2}-x+5)(x^{2}+3x-9)
limit as x approaches 2+of (-2)/(x^2-4)	\lim\:_{x\to\:2+}(\frac{-2}{x^{2}-4})
limit as x approaches 0 of-3/(x^2)	\lim\:_{x\to\:0}(-\frac{3}{x^{2}})
derivative of arctan(sin(4x))	derivative\:\arctan(\sin(4x))
(\partial)/(\partial x)(2+xln(xy-7))	\frac{\partial\:}{\partial\:x}(2+x\ln(xy-7))
derivative of x^2sqrt(x-1)	\frac{d}{dx}(x^{2}\sqrt{x-1})
integral of (3x^2+8x-12)/(x^3+7x+12x)	\int\:\frac{3x^{2}+8x-12}{x^{3}+7x+12x}dx
integral of (3^{x+2})/(4^{x-1)}	\int\:\frac{3^{x+2}}{4^{x-1}}dx
integral of xcos(6x)	\int\:x\cos(6x)dx
integral of x^{-2}e^{1/x}	\int\:x^{-2}e^{\frac{1}{x}}dx
derivative of 3x-8	derivative\:3x-8
(5y-2x)y^'-2y=0	(5y-2x)y^{\prime\:}-2y=0
tangent of f(x)=xsqrt(x^2+60),\at x=2	tangent\:f(x)=x\sqrt{x^{2}+60},\at\:x=2
(\partial)/(\partial x)((3-x)(3-y)(x+y-3))	\frac{\partial\:}{\partial\:x}((3-x)(3-y)(x+y-3))
(d^2)/(dx^2)((3+2x)e^{-3x})	\frac{d^{2}}{dx^{2}}((3+2x)e^{-3x})
derivative of x(-3x^{-4})	derivative\:x(-3x^{-4})
integral of-5sin^3(x)cos^2(x)	\int\:-5\sin^{3}(x)\cos^{2}(x)dx
tangent of f(x)=-3x^2+8x+1,\at x=-2	tangent\:f(x)=-3x^{2}+8x+1,\at\:x=-2
derivative of 3^{-x}	derivative\:3^{-x}
limit as x approaches 6 of-x^2+4x-3	\lim\:_{x\to\:6}(-x^{2}+4x-3)
integral of csc(x)sec^2(x)	\int\:\csc(x)\sec^{2}(x)dx
integral of (x^2+1)/(x^2-5x+6)	\int\:\frac{x^{2}+1}{x^{2}-5x+6}dx
(\partial)/(\partial x)(5e^{2x})	\frac{\partial\:}{\partial\:x}(5e^{2x})
derivative of y=(x^4)/4+2/9 x^3-x^2+9x-5	derivative\:y=\frac{x^{4}}{4}+\frac{2}{9}x^{3}-x^{2}+9x-5
maclaurin ((2x))/(1+x^4)	maclaurin\:\frac{(2x)}{1+x^{4}}
derivative of sqrt(7-4x)	derivative\:\sqrt{7-4x}
derivative of e^{4xsin(2x})	\frac{d}{dx}(e^{4x\sin(2x)})
derivative of f(x)=ln(196sin^2(x))	derivative\:f(x)=\ln(196\sin^{2}(x))
(dy)/(dx)=sqrt(6y)e^{x+7}	\frac{dy}{dx}=\sqrt{6y}e^{x+7}
integral from 1 to 4 of 4x^2-2x	\int\:_{1}^{4}4x^{2}-2xdx
derivative of x3^x	\frac{d}{dx}(x3^{x})
sum from n=1 to infinity of n^32^{-n}	\sum\:_{n=1}^{\infty\:}n^{3}2^{-n}
integral of (1/(x^2)+4/(xsqrt(x))+2)	\int\:(\frac{1}{x^{2}}+\frac{4}{x\sqrt{x}}+2)dx
derivative of (3x/(x^2-1))	\frac{d}{dx}(\frac{3x}{x^{2}-1})
y^{''}+6y^'+34y=0,y(0)=-1,y^'(0)=13	y^{\prime\:\prime\:}+6y^{\prime\:}+34y=0,y(0)=-1,y^{\prime\:}(0)=13
derivative of f(x)=(28)/x	derivative\:f(x)=\frac{28}{x}
limit as x approaches 1 of 2x+1	\lim\:_{x\to\:1}(2x+1)
limit as x approaches 0-of (e^{1/x})/x	\lim\:_{x\to\:0-}(\frac{e^{\frac{1}{x}}}{x})
integral from-pi to pi of sin(mx)cos(nx)	\int\:_{-π}^{π}\sin(mx)\cos(nx)dx
derivative of 9e^xsqrt(x)	derivative\:9e^{x}\sqrt{x}
(d^{10})/(dx^{10)}(sin(x))	\frac{d^{10}}{dx^{10}}(\sin(x))
derivative of (x-1^2)	\frac{d}{dx}((x-1)^{2})
derivative of a+x	\frac{d}{dx}(a+x)
tangent of f(x)=sqrt(x)	tangent\:f(x)=\sqrt{x}
(\partial)/(\partial x)((4x+3t)/(x-2t))	\frac{\partial\:}{\partial\:x}(\frac{4x+3t}{x-2t})
derivative of 2x^4ln(x)	derivative\:2x^{4}\ln(x)
integral from 0 to 1 of pi(x^2-x)	\int\:_{0}^{1}π(x^{2}-x)dx
integral from 0 to 1 of ((1+e^x))/(e^x)	\int\:_{0}^{1}\frac{(1+e^{x})}{e^{x}}dx
integral of (x^2)/(sqrt(9-4x^2))	\int\:\frac{x^{2}}{\sqrt{9-4x^{2}}}dx
derivative of a^x*x^a	\frac{d}{dx}(a^{x}\cdot\:x^{a})
x+2xy^2+e^{x^2}y(dy)/(dx)=0	x+2xy^{2}+e^{x^{2}}y\frac{dy}{dx}=0
integral of 2(y-1)	\int\:2(y-1)dy
integral of x^2cos(nx)	\int\:x^{2}\cos(nx)dx
integral from-3 to 0 of x^3	\int\:_{-3}^{0}x^{3}dx
derivative of 3t^2-27	derivative\:3t^{2}-27
integral of csc^4(2x)	\int\:\csc^{4}(2x)dx
integral of (9+5x)/(1+x^2)	\int\:\frac{9+5x}{1+x^{2}}dx
derivative of sqrt(3x+x^2)	\frac{d}{dx}(\sqrt{3x+x^{2}})
(\partial)/(\partial x)(2x(1-x^2y^2))	\frac{\partial\:}{\partial\:x}(2x(1-x^{2}y^{2}))
derivative of 4x^3+3x^2+2x	\frac{d}{dx}(4x^{3}+3x^{2}+2x)
derivative of sqrt(x^3-100x+1)	\frac{d}{dx}(\sqrt{x^{3}-100x+1})
(d^2)/(dx^2)(e^{7x-4})	\frac{d^{2}}{dx^{2}}(e^{7x-4})
integral of arctan(2t)	\int\:\arctan(2t)dt
derivative of f(x)=x^4-8x^3	derivative\:f(x)=x^{4}-8x^{3}
derivative of f(x)=3x^3-9x	derivative\:f(x)=3x^{3}-9x
limit as x approaches 1 of (1-x^2)/(x+1)	\lim\:_{x\to\:1}(\frac{1-x^{2}}{x+1})
integral of (sin^7(11x))/(cos^4(11x))	\int\:\frac{\sin^{7}(11x)}{\cos^{4}(11x)}dx
derivative of y=(6x+1)^2	derivative\:y=(6x+1)^{2}
(\partial)/(\partial x)(xsin(xyz))	\frac{\partial\:}{\partial\:x}(x\sin(xyz))
integral of ln(e)	\int\:\ln(e)
integral of sin(2ax)	\int\:\sin(2ax)dx
integral of 1/(sqrt(3-4x^2))	\int\:\frac{1}{\sqrt{3-4x^{2}}}dx
y^{''}-y=t-4e^{-t}	y^{\prime\:\prime\:}-y=t-4e^{-t}
integral of 8sec^3(2x)	\int\:8\sec^{3}(2x)dx
integral of 4xe^{(2x)/3}	\int\:4xe^{\frac{2x}{3}}dx
integral from 1 to infinity of e^{-3x}	\int\:_{1}^{\infty\:}e^{-3x}dx
integral from 3 to infinity of 1/(x-2)	\int\:_{3}^{\infty\:}\frac{1}{x-2}dx
integral of x^2+2x+3	\int\:x^{2}+2x+3dx
derivative of (x^2+y^2^6)	\frac{d}{dx}((x^{2}+y^{2})^{6})
(\partial}{\partial v}(\frac{u+v)/2)	\frac{\partial\:}{\partial\:v}(\frac{u+v}{2})
y^{''''}-9y^{''}+20y=0	y^{\prime\:\prime\:\prime\:\prime\:}-9y^{\prime\:\prime\:}+20y=0
integral of (10\sqrt[3]{5x-2})/3	\int\:\frac{10\sqrt[3]{5x-2}}{3}dx
integral from 0 to 3 of sqrt(1+16x^2)	\int\:_{0}^{3}\sqrt{1+16x^{2}}dx
inverse oflaplace x^2	inverselaplace\:x^{2}
(4xy^2+3y)dx+(4x^2y+3x)dy=0	(4xy^{2}+3y)dx+(4x^{2}y+3x)dy=0
inverse oflaplace (2250)/(5x^2+x)	inverselaplace\:\frac{2250}{5x^{2}+x}
slope of (-12)(-1-3)	slope\:(-12)(-1-3)
derivative of 4e^xcos(x)	derivative\:4e^{x}\cos(x)
(x+y)^2dx+(2xy+x^2-9)dy=0,y(1)=1	(x+y)^{2}dx+(2xy+x^{2}-9)dy=0,y(1)=1
derivative of (x^2/((1+x)^4))	\frac{d}{dx}(\frac{x^{2}}{(1+x)^{4}})
integral from 0 to 2 of x*3^x	\int\:_{0}^{2}x\cdot\:3^{x}dx
integral of cot^3(x)*csc^2(x)	\int\:\cot^{3}(x)\cdot\:\csc^{2}(x)dx
integral of 4x^3+x^2	\int\:4x^{3}+x^{2}dx
integral of x^3sqrt(2x+1)	\int\:x^{3}\sqrt{2x+1}dx
derivative of sin(x+cos(x)+tan(x))	\frac{d}{dx}(\sin(x)+\cos(x)+\tan(x))
d/(dy)(ln(sqrt(xy)))	\frac{d}{dy}(\ln(\sqrt{xy}))
derivative of (450t)/((t^2+6)^3)	derivative\:\frac{450t}{(t^{2}+6)^{3}}
tangent of y=(2x)/(x^2+1),(0,0)	tangent\:y=\frac{2x}{x^{2}+1},(0,0)

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