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Popular Calculus Problems

(\partial)/(\partial x)(xy^2-2xy-2x^2-3x)	\frac{\partial\:}{\partial\:x}(xy^{2}-2xy-2x^{2}-3x)
(dy)/(dx)=y^2e^{-2x}	\frac{dy}{dx}=y^{2}e^{-2x}
derivative of 5/2 x^{-2}	\frac{d}{dx}(\frac{5}{2}x^{-2})
roots e^{mx}	roots\:e^{mx}
integral of \sqrt[5]{4^{3x}}	\int\:\sqrt[5]{4^{3x}}dx
area y=9-0.25x^2,y=1,2<x<5	area\:y=9-0.25x^{2},y=1,2<x<5
(\partial)/(\partial x)(x/(x^2+9y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+9y^{2}})
integral of (x+sqrt(1+x^2))^6	\int\:(x+\sqrt{1+x^{2}})^{6}dx
integral of sec^4(5x)tan(5x)	\int\:\sec^{4}(5x)\tan(5x)dx
limit as x approaches 2 of sin((pix)/2)	\lim\:_{x\to\:2}(\sin(\frac{pix}{2}))
derivative of 5x^2e^{-x}	\frac{d}{dx}(5x^{2}e^{-x})
derivative of (r^6-9r)e^r	derivative\:(r^{6}-9r)e^{r}
integral of (8sqrt(x))/(x-1)	\int\:\frac{8\sqrt{x}}{x-1}dx
f(x)=6x^3	f(x)=6x^{3}
d/(dz)(z/((z^2+R^2)^{3/2)})	\frac{d}{dz}(\frac{z}{(z^{2}+R^{2})^{\frac{3}{2}}})
integral of 0/x	\int\:\frac{0}{x}dx
derivative of (e^x/(x^7))	\frac{d}{dx}(\frac{e^{x}}{x^{7}})
integral of a^{5x}	\int\:a^{5x}dx
integral from 0 to pi/2 of 2-sin(x)	\int\:_{0}^{\frac{π}{2}}2-\sin(x)dx
(d^2)/(dx^2)(x(1+x^2)^{10})	\frac{d^{2}}{dx^{2}}(x(1+x^{2})^{10})
derivative of 3x^{-5}	derivative\:3x^{-5}
(\partial)/(\partial v)(usin(v))	\frac{\partial\:}{\partial\:v}(u\sin(v))
limit as x approaches pi of sec(x)	\lim\:_{x\to\:π}(\sec(x))
integral of ((2x+4))/(x^2+5x-6)	\int\:\frac{(2x+4)}{x^{2}+5x-6}dx
integral of 1/(sqrt(t^2-6t+25))	\int\:\frac{1}{\sqrt{t^{2}-6t+25}}dt
derivative of cos(ln(3x))	\frac{d}{dx}(\cos(\ln(3x)))
integral of sqrt(x)-x	\int\:\sqrt{x}-xdx
area 2-x^2,-x	area\:2-x^{2},-x
limit as x approaches-1 of 4x^2	\lim\:_{x\to\:-1}(4x^{2})
(\partial)/(\partial x)(4x^2e^{ay}+3e^{bx})	\frac{\partial\:}{\partial\:x}(4x^{2}e^{ay}+3e^{bx})
integral of (tan^3(x))/(cos^3(x))	\int\:\frac{\tan^{3}(x)}{\cos^{3}(x)}dx
integral of sin(cos(x))sin(x)	\int\:\sin(\cos(x))\sin(x)dx
(\partial)/(\partial u)(uv^2)	\frac{\partial\:}{\partial\:u}(uv^{2})
derivative of 7/(x-3)	\frac{d}{dx}(\frac{7}{x-3})
derivative of-3cos(3x)	derivative\:-3\cos(3x)
derivative of f(x)=(x^2)/(x^3+1)	derivative\:f(x)=\frac{x^{2}}{x^{3}+1}
integral from 2 to 7 of 1/(sqrt(x-2))	\int\:_{2}^{7}\frac{1}{\sqrt{x-2}}dx
derivative of f(x)=e^{4xsin(2x)}	derivative\:f(x)=e^{4x\sin(2x)}
(\partial)/(\partial x)((e^x)/(u(x)+x^2))	\frac{\partial\:}{\partial\:x}(\frac{e^{x}}{u(x)+x^{2}})
y^{''}-9/x y^'+(34)/(x^2)y=0	y^{\prime\:\prime\:}-\frac{9}{x}y^{\prime\:}+\frac{34}{x^{2}}y=0
(dy)/(dx)=5y+2	\frac{dy}{dx}=5y+2
derivative of (6x+2x^2)/((3+2x)^2)	derivative\:\frac{6x+2x^{2}}{(3+2x)^{2}}
integral of (x+1)/(sqrt(x^2-9))	\int\:\frac{x+1}{\sqrt{x^{2}-9}}dx
(\partial)/(\partial x)(-3x^2y^3sin(x^3y^3))	\frac{\partial\:}{\partial\:x}(-3x^{2}y^{3}\sin(x^{3}y^{3}))
derivative of f(0)= x/(x^2+1)	derivative\:f(0)=\frac{x}{x^{2}+1}
integral of e^{-0.01t}	\int\:e^{-0.01t}dt
derivative of 1/(1+\|x\|+1/(1+\|x-3\|))	\frac{d}{dx}(\frac{1}{1+\left\|x\right\|}+\frac{1}{1+\left\|x-3\right\|})
(\partial)/(\partial y)(2x-3yz)	\frac{\partial\:}{\partial\:y}(2x-3yz)
d/(d{r)}((200{r}({r}+2))/((2+3{r))^2})	\frac{d}{d{r}}(\frac{200{r}({r}+2)}{(2+3{r})^{2}})
tangent of y=sqrt(9-10x),\at x=-1	tangent\:y=\sqrt{9-10x},\at\:x=-1
derivative of 2xy^3	\frac{d}{dx}(2xy^{3})
(\partial)/(\partial y)(e^{sin(x+y)})	\frac{\partial\:}{\partial\:y}(e^{\sin(x+y)})
tangent of f(x)=1+4csc(x),\at x=-pi/3	tangent\:f(x)=1+4\csc(x),\at\:x=-\frac{π}{3}
sum from n=1 to infinity of 2/(3n+10)	\sum\:_{n=1}^{\infty\:}\frac{2}{3n+10}
integral from 1 to 2 of 4xsqrt(4x^2+4)	\int\:_{1}^{2}4x\sqrt{4x^{2}+4}dx
integral of (3x^4-5x^2+6x)	\int\:(3x^{4}-5x^{2}+6x)dx
limit as x approaches 0 of (\|x+1\|-\|x-1\|)/x	\lim\:_{x\to\:0}(\frac{\left\|x+1\right\|-\left\|x-1\right\|}{x})
sum from n=1 to infinity of 8	\sum\:_{n=1}^{\infty\:}8
(\partial)/(\partial v)(u^2+v^2)	\frac{\partial\:}{\partial\:v}(u^{2}+v^{2})
laplacetransform 1-e^{-0.4t}	laplacetransform\:1-e^{-0.4t}
integral of 1/(5+2x)	\int\:\frac{1}{5+2x}dx
tangent of (x^2+1)^{(x+1)}	tangent\:(x^{2}+1)^{(x+1)}
derivative of (2x+5/3)	\frac{d}{dx}(\frac{2x+5}{3})
f(x)=xarctan(x)	f(x)=x\arctan(x)
limit as x approaches 0 of 1/(x^{2/3)}	\lim\:_{x\to\:0}(\frac{1}{x^{\frac{2}{3}}})
d/(ds)(ln(s^2+1))	\frac{d}{ds}(\ln(s^{2}+1))
integral of (4x^3+7)	\int\:(4x^{3}+7)dx
(\partial)/(\partial x)(zsin(x)+y^2)	\frac{\partial\:}{\partial\:x}(z\sin(x)+y^{2})
integral of x/((x+2)^{2/3)}	\int\:\frac{x}{(x+2)^{\frac{2}{3}}}dx
limit as x approaches 0 of cos(pi/2)	\lim\:_{x\to\:0}(\cos(\frac{π}{2}))
derivative of y=8e^xcos(x)	derivative\:y=8e^{x}\cos(x)
integral of ((x+1))/x	\int\:\frac{(x+1)}{x}dx
integral of 1/(sqrt(e^{2x)+1)}	\int\:\frac{1}{\sqrt{e^{2x}+1}}dx
y^{''}+2y^'+2y=sin(x),y(0)=1,y^'(0)=-1	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(x),y(0)=1,y^{\prime\:}(0)=-1
y^'=x+y,y(0)=7	y^{\prime\:}=x+y,y(0)=7
derivative of (4x^2+2x+8/(sqrt(x)))	\frac{d}{dx}(\frac{4x^{2}+2x+8}{\sqrt{x}})
derivative of 2x^{-2}	\frac{d}{dx}(2x^{-2})
y^{''}-8y^'+20y=0	y^{\prime\:\prime\:}-8y^{\prime\:}+20y=0
limit as x approaches pi of e^{cos(3x)}	\lim\:_{x\to\:π}(e^{\cos(3x)})
integral from 1 to sqrt(2 of)x5^{(x^2)}	\int\:_{1}^{\sqrt{2}}x5^{(x^{2})}dx
limit as x approaches 0 of (3x^2-2x)/x	\lim\:_{x\to\:0}(\frac{3x^{2}-2x}{x})
integral of (sqrt(49-x^2))/(x^2)	\int\:\frac{\sqrt{49-x^{2}}}{x^{2}}dx
integral of (e^{2x}-6e^x)/(e^{2x)+11}	\int\:\frac{e^{2x}-6e^{x}}{e^{2x}+11}dx
tangent of f(x)=sqrt(20x+5)	tangent\:f(x)=\sqrt{20x+5}
integral of (e^{1/(x^4)})/(x^5)	\int\:\frac{e^{\frac{1}{x^{4}}}}{x^{5}}dx
limit as x approaches 2 of (4x-3)/(x+2)	\lim\:_{x\to\:2}(\frac{4x-3}{x+2})
((x^4)/4)^'	(\frac{x^{4}}{4})^{\prime\:}
inverse oflaplace (360)/(2s^2+10s+8)	inverselaplace\:\frac{360}{2s^{2}+10s+8}
(\partial)/(\partial x)(ye^{3x}*3)	\frac{\partial\:}{\partial\:x}(ye^{3x}\cdot\:3)
tangent of y= 7/(x^2+3),(2,1)	tangent\:y=\frac{7}{x^{2}+3},(2,1)
limit as x approaches 2 of x^3+4x^2-3x-6	\lim\:_{x\to\:2}(x^{3}+4x^{2}-3x-6)
integral of 1/(t^2sqrt(5-t^2))	\int\:\frac{1}{t^{2}\sqrt{5-t^{2}}}dt
integral from 1 to 4 of 3/(x^2)	\int\:_{1}^{4}\frac{3}{x^{2}}dx
(\partial)/(\partial x)(x+y+xy+x/y+y/x)	\frac{\partial\:}{\partial\:x}(x+y+xy+\frac{x}{y}+\frac{y}{x})
y^{''}+y=k	y^{\prime\:\prime\:}+y=k
integral from 4 to 5 of x^2sqrt(x-4)	\int\:_{4}^{5}x^{2}\sqrt{x-4}dx
(\partial)/(\partial x)((20)/(8+x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{20}{8+x^{2}+y^{2}})
(\partial)/(\partial t)((8.31t)/(V(t)))	\frac{\partial\:}{\partial\:t}(\frac{8.31t}{V(t)})
limit as x approaches 2 of (2x-6)/(x-1)	\lim\:_{x\to\:2}(\frac{2x-6}{x-1})
laplacetransform te^{8t}	laplacetransform\:te^{8t}

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