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Popular Calculus Problems

derivative of 200	\frac{d}{dx}(200)
slope of xsqrt(x)	slope\:x\sqrt{x}
derivative of ae^{-x}	\frac{d}{dx}(ae^{-x})
(\partial)/(\partial x)(e^{6y}sin(-6x))	\frac{\partial\:}{\partial\:x}(e^{6y}\sin(-6x))
sum from n=1 to infinity of 17-7/(n^3)	\sum\:_{n=1}^{\infty\:}17-\frac{7}{n^{3}}
integral of sinh(x)cosh^4(x)	\int\:\sinh(x)\cosh^{4}(x)dx
area y=2x^2,y=3-x	area\:y=2x^{2},y=3-x
integral of (5x^2+2/(x^4)-3\sqrt[3]{x})	\int\:(5x^{2}+\frac{2}{x^{4}}-3\sqrt[3]{x})dx
limit as x approaches 5 of (4x)/(x-5)	\lim\:_{x\to\:5}(\frac{4x}{x-5})
y^'=(t+y)^2-1,y(3)=6	y^{\prime\:}=(t+y)^{2}-1,y(3)=6
integral of ((x^2+3x-4))/(x^3-4x^2+4x)	\int\:\frac{(x^{2}+3x-4)}{x^{3}-4x^{2}+4x}dx
area y=4x^2,x=1,y=0	area\:y=4x^{2},x=1,y=0
inverse oflaplace (2e^{-2s})/(5s^2+45)	inverselaplace\:\frac{2e^{-2s}}{5s^{2}+45}
derivative of y=e^{((3x^2))/2}	derivative\:y=e^{\frac{(3x^{2})}{2}}
derivative of (x^{63}-1)/(x-1)	derivative\:\frac{x^{63}-1}{x-1}
derivative of 3/(3x+1)	\frac{d}{dx}(\frac{3}{3x+1})
limit as x approaches infinity of 1/e	\lim\:_{x\to\:\infty\:}(\frac{1}{e})
derivative of y=e^{x^3}	derivative\:y=e^{x^{3}}
(\partial)/(\partial x)(arcsin(xy))	\frac{\partial\:}{\partial\:x}(\arcsin(xy))
derivative of x^2sin^3(3x)	derivative\:x^{2}\sin^{3}(3x)
derivative of x^{10}arctan(x)	derivative\:x^{10}\arctan(x)
(\partial)/(\partial y)(15-5(y+3)^2)	\frac{\partial\:}{\partial\:y}(15-5(y+3)^{2})
(\partial)/(\partial x)(7x^3cos(7x^2y))	\frac{\partial\:}{\partial\:x}(7x^{3}\cos(7x^{2}y))
(\partial)/(\partial y)(3x^4y^2+1)	\frac{\partial\:}{\partial\:y}(3x^{4}y^{2}+1)
integral from-2 to 3 of (22)/(x^4)	\int\:_{-2}^{3}\frac{22}{x^{4}}dx
laplacetransform 1/3	laplacetransform\:\frac{1}{3}
integral of 343x^2cos(7x)	\int\:343x^{2}\cos(7x)dx
tangent of (e^x)/(x+1),\at x=0	tangent\:\frac{e^{x}}{x+1},\at\:x=0
integral of 8cos^4(θ)sin(θ)	\int\:8\cos^{4}(θ)\sin(θ)dθ
integral of 5/(16+x^2)	\int\:\frac{5}{16+x^{2}}dx
derivative of ln(ln(8s))	derivative\:\ln(\ln(8s))
derivative of f(x)=4x^4-x^6	derivative\:f(x)=4x^{4}-x^{6}
derivative of y=(6x^3+3x+1)^{10}	derivative\:y=(6x^{3}+3x+1)^{10}
integral from 0 to 1 of (x+y)	\int\:_{0}^{1}(x+y)dx
integral of (e^tsqrt(e^t+2))/(e^t+6)	\int\:\frac{e^{t}\sqrt{e^{t}+2}}{e^{t}+6}dt
y^{''}-1y^'-12y=0	y^{\prime\:\prime\:}-1y^{\prime\:}-12y=0
(\partial)/(\partial x)(xy-y+sin(1))	\frac{\partial\:}{\partial\:x}(xy-y+\sin(1))
integral from 0 to 2 of 2^{-θ}	\int\:_{0}^{2}2^{-θ}dθ
integral of sin^3(4x)sqrt(cos(4x))	\int\:\sin^{3}(4x)\sqrt{\cos(4x)}dx
(\partial)/(\partial x)(x^{-1}y^2+xy^2+5xy)	\frac{\partial\:}{\partial\:x}(x^{-1}y^{2}+xy^{2}+5xy)
integral from 1 to 16 of 1/(8-sqrt(x))	\int\:_{1}^{16}\frac{1}{8-\sqrt{x}}dx
(dy)/(dx)+2xy=y+4x-2	\frac{dy}{dx}+2xy=y+4x-2
derivative of (4x^3+5^{3/2})	\frac{d}{dx}((4x^{3}+5)^{\frac{3}{2}})
(\partial}{\partial x}(\frac{x^2-1)/y)	\frac{\partial\:}{\partial\:x}(\frac{x^{2}-1}{y})
limit as x approaches 3 of 2x^{x^2}-3x+2	\lim\:_{x\to\:3}(2x^{x^{2}}-3x+2)
integral of-32x+12	\int\:-32x+12dx
y^{''}+y=2xcos(x)	y^{\prime\:\prime\:}+y=2x\cos(x)
(\partial)/(\partial y)(sqrt(3x+4y))	\frac{\partial\:}{\partial\:y}(\sqrt{3x+4y})
derivative of (sqrt(x)/(2-x))	\frac{d}{dx}(\frac{\sqrt{x}}{2-x})
derivative of [x+(x+sin^2(x)^3]^6)	\frac{d}{dx}([x+(x+\sin^{2}(x))^{3}]^{6})
integral of 2^{e^x}(1+2^{e^x})^5e^x	\int\:2^{e^{x}}(1+2^{e^{x}})^{5}e^{x}dx
derivative of (sec(x)/x)	\frac{d}{dx}(\frac{\sec(x)}{x})
derivative of (ln(3)^x)	\frac{d}{dx}((\ln(3))^{x})
integral of sqrt(x/2)	\int\:\sqrt{\frac{x}{2}}dx
tangent of f(x)=3x^2+9x^3-5x,\at x=-4	tangent\:f(x)=3x^{2}+9x^{3}-5x,\at\:x=-4
inverse oflaplace 1/(2(s+2))	inverselaplace\:\frac{1}{2(s+2)}
taylor sqrt(x+3)	taylor\:\sqrt{x+3}
d/(ds)(3/(s^2+9))	\frac{d}{ds}(\frac{3}{s^{2}+9})
integral of arctan(x)	\int\:\arctan(x)dx
cos^2(t)(dy)/(dt)=1	\cos^{2}(t)\frac{dy}{dt}=1
derivative of (3x-1/(sqrt(x)))	\frac{d}{dx}(\frac{3x-1}{\sqrt{x}})
(\partial)/(\partial x)(sqrt(2x^2+3y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{2x^{2}+3y^{2}})
(d^2)/(dx^2)(x^2)	\frac{d^{2}}{dx^{2}}(x^{2})
integral from 0 to 16 of sin(sqrt(x))	\int\:_{0}^{16}\sin(\sqrt{x})dx
integral of sin^n(x)	\int\:\sin^{n}(x)dx
derivative of x^{9sin(x})	\frac{d}{dx}(x^{9\sin(x)})
integral of zsqrt(4z^2+8)	\int\:z\sqrt{4z^{2}+8}dz
(dy)/(dx)=((x-4))/(y-6)	\frac{dy}{dx}=\frac{(x-4)}{y-6}
area y=10+9x-x^2,y=-3x+46,[6,15+1/3 ]	area\:y=10+9x-x^{2},y=-3x+46,[6,15+\frac{1}{3}]
ty^'=t^3+7t^3y	ty^{\prime\:}=t^{3}+7t^{3}y
derivative of tan(x+cot(x))	\frac{d}{dx}(\tan(x)+\cot(x))
integral of (9+x)/x	\int\:\frac{9+x}{x}dx
y^'=-(4x)/y	y^{\prime\:}=-\frac{4x}{y}
sum from n=0 to infinity of 8/(n!)	\sum\:_{n=0}^{\infty\:}\frac{8}{n!}
y^'=1-y^2	y^{\prime\:}=1-y^{2}
integral of x+x^2	\int\:x+x^{2}dx
integral of 5x^3	\int\:5x^{3}dx
derivative of (1+sin(x)cos(2x))	\frac{d}{dx}((1+\sin(x))\cos(2x))
sum from n=0 to infinity of (5n)/(2n-1)	\sum\:_{n=0}^{\infty\:}\frac{5n}{2n-1}
y^'+3y=e^{-3x}	y^{\prime\:}+3y=e^{-3x}
integral from 2 to 3 of (4+2x)^2	\int\:_{2}^{3}(4+2x)^{2}dx
(\partial)/(\partial x)(x^9yz^2+9yz)	\frac{\partial\:}{\partial\:x}(x^{9}yz^{2}+9yz)
(\partial)/(\partial y)(y^2sqrt(x))	\frac{\partial\:}{\partial\:y}(y^{2}\sqrt{x})
integral of 1/(1+2u)	\int\:\frac{1}{1+2u}du
integral of (3x^2-4x+7)	\int\:(3x^{2}-4x+7)dx
derivative of f(x)=((x^2+4)/(x^2-4))^4	derivative\:f(x)=(\frac{x^{2}+4}{x^{2}-4})^{4}
(dy)/(dx)=((xy+3x-y-3))/((xy-2x+4y-8))	\frac{dy}{dx}=\frac{(xy+3x-y-3)}{(xy-2x+4y-8)}
integral of x^2+6x^{-3/2}	\int\:x^{2}+6x^{-\frac{3}{2}}dx
derivative of (2-5x/(3x^{1/3)})	\frac{d}{dx}(\frac{2-5x}{3x^{\frac{1}{3}}})
limit as x approaches infinity of ((25x+7)sqrt(5x^2+2))/(5x^2+2)	\lim\:_{x\to\:\infty\:}(\frac{(25x+7)\sqrt{5x^{2}+2}}{5x^{2}+2})
integral of 14^x	\int\:14^{x}dx
tangent of f(x)=4+3ln(x),\at x=1	tangent\:f(x)=4+3\ln(x),\at\:x=1
limit as x approaches 2 of 1/x	\lim\:_{x\to\:2}(\frac{1}{x})
integral of (x^3+x+1)/(x^2-4x+3)	\int\:\frac{x^{3}+x+1}{x^{2}-4x+3}dx
(\partial)/(\partial z)(xye^z+x-z^2-3)	\frac{\partial\:}{\partial\:z}(xye^{z}+x-z^{2}-3)
integral of 9/(x^2+4)	\int\:\frac{9}{x^{2}+4}dx
(\partial)/(\partial x)(6e^xln(y))	\frac{\partial\:}{\partial\:x}(6e^{x}\ln(y))
integral of xsin(x^2+1)	\int\:x\sin(x^{2}+1)dx
integral of (3n-4)/(n^2-2n)	\int\:\frac{3n-4}{n^{2}-2n}
integral of ((1+xy)e^{xy})	\int\:((1+xy)e^{xy})dx

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