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Popular Calculus Problems

derivative of sqrt(1/(x^2-2))	\frac{d}{dx}(\sqrt{\frac{1}{x^{2}-2}})
(\partial)/(\partial x)(x^2+y^2+2xy)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+2xy)
integral of 7e^{-0.8x}	\int\:7e^{-0.8x}dx
limit as x approaches infinity of x 1/2	\lim\:_{x\to\:\infty\:}(x\frac{1}{2})
limit as x approaches 0 of x^2csc^2(x/2)	\lim\:_{x\to\:0}(x^{2}\csc^{2}(\frac{x}{2}))
slope of (-9,6),(-6,-9)	slope\:(-9,6),(-6,-9)
integral of r^4(7-(r^5)/(10))^3	\int\:r^{4}(7-\frac{r^{5}}{10})^{3}dr
y^'=(3t^2-e^t)/(2y-5)	y^{\prime\:}=\frac{3t^{2}-e^{t}}{2y-5}
integral of \sqrt[3]{t}(5t^2-3t+2)	\int\:\sqrt[3]{t}(5t^{2}-3t+2)dt
sum from n=1 to infinity of 3n+1	\sum\:_{n=1}^{\infty\:}3n+1
integral from 0 to 1 of sqrt(1+(2x)^2)	\int\:_{0}^{1}\sqrt{1+(2x)^{2}}dx
derivative of y=3+5sqrt(x)	derivative\:y=3+5\sqrt{x}
(\partial)/(\partial x)(cosh(x))	\frac{\partial\:}{\partial\:x}(\cosh(x))
integral of (5r^2)/(r+1)	\int\:\frac{5r^{2}}{r+1}dr
tangent of f(x)=9x^2+5	tangent\:f(x)=9x^{2}+5
sum from n=0 to infinity of 1/(n^{3/2)}	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{\frac{3}{2}}}
area (x^3-11x^2+30x),(-x^3+11x^2-30x)	area\:(x^{3}-11x^{2}+30x),(-x^{3}+11x^{2}-30x)
derivative of log_{3}((x^2/(x+1)))	\frac{d}{dx}(\log_{3}(\frac{x^{2}}{x+1}))
(dy)/(dx)=-4(y-3)	\frac{dy}{dx}=-4(y-3)
(\partial)/(\partial x)(2x+y^6)	\frac{\partial\:}{\partial\:x}(2x+y^{6})
integral of sin^2(x/2)	\int\:\sin^{2}(\frac{x}{2})dx
derivative of f(x)=ln(x+sqrt(3+x^2))	derivative\:f(x)=\ln(x+\sqrt{3+x^{2}})
integral of-x/(y^2)	\int\:-\frac{x}{y^{2}}dy
(dy)/(dx)+10(tan(10x))y=-cos(10x)	\frac{dy}{dx}+10(\tan(10x))y=-\cos(10x)
integral of ((x^3))/(sqrt(x^2+100))	\int\:\frac{(x^{3})}{\sqrt{x^{2}+100}}dx
derivative of e^{rx}	derivative\:e^{rx}
derivative of-e^{-x}x^2+6e^{-x}x-6e^{-x}	\frac{d}{dx}(-e^{-x}x^{2}+6e^{-x}x-6e^{-x})
integral of cot^3(10x)	\int\:\cot^{3}(10x)dx
2(d^2y)/(dx^2)+2(dy)/(dx)+y=1	2\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}+y=1
derivative of cos(x^3+2x)	\frac{d}{dx}(\cos(x^{3}+2x))
derivative of 3x^{4/3}-2x^{1/7}	derivative\:3x^{\frac{4}{3}}-2x^{\frac{1}{7}}
limit as x approaches-3 of ((x^2+7x+12))/(x^2-9)	\lim\:_{x\to\:-3}(\frac{(x^{2}+7x+12)}{x^{2}-9})
limit as x approaches 3 of (x^2-9)/(x+1)	\lim\:_{x\to\:3}(\frac{x^{2}-9}{x+1})
integral of 4cos(6x)	\int\:4\cos(6x)dx
integral of-(3x)/2	\int\:-\frac{3x}{2}dx
integral of 2/(x^3+x)	\int\:\frac{2}{x^{3}+x}dx
integral from 0 to 2 of sqrt(4-x^2)	\int\:_{0}^{2}\sqrt{4-x^{2}}dx
(\partial)/(\partial y)(xy^2)	\frac{\partial\:}{\partial\:y}(xy^{2})
derivative of 3ln(2x)	derivative\:3\ln(2x)
integral of (sin^2(1/x))/(x^2)	\int\:\frac{\sin^{2}(\frac{1}{x})}{x^{2}}dx
derivative of 10^6x^2e^{-x}	\frac{d}{dx}(10^{6}\cdot\:x^{2}\cdot\:e^{-x})
integral of (e^{2t})/(sqrt(e^{2t)+4)}	\int\:\frac{e^{2t}}{\sqrt{e^{2t}+4}}dt
d/(d{y)}(10e^{{x}}sin({y}){z}^3)	\frac{d}{d{y}}(10e^{{x}}\sin({y}){z}^{3})
d/(dt)(5t^{-3/5})	\frac{d}{dt}(5t^{-\frac{3}{5}})
integral of 1/(x+sqrt(x))	\int\:\frac{1}{x+\sqrt{x}}dx
integral of ((x^2))/(1+x^3)	\int\:\frac{(x^{2})}{1+x^{3}}dx
limit as x approaches-1 of 3x^2-2x-1	\lim\:_{x\to\:-1}(3x^{2}-2x-1)
tangent of f(x)=3-x^2+2x	tangent\:f(x)=3-x^{2}+2x
tangent of f(x)=8x^2+4x-6,\at x=-3	tangent\:f(x)=8x^{2}+4x-6,\at\:x=-3
integral of (u-2u^2)/(sqrt(u))	\int\:\frac{u-2u^{2}}{\sqrt{u}}du
integral of ae^x	\int\:ae^{x}dx
integral of 8/(sqrt(e^x-2))	\int\:\frac{8}{\sqrt{e^{x}-2}}dx
integral from-infinity to 15 of re^{r/5}	\int\:_{-\infty\:}^{15}re^{\frac{r}{5}}dr
derivative of 3x^2+8	\frac{d}{dx}(3x^{2}+8)
integral from-1 to 2 of (3x^2+2)	\int\:_{-1}^{2}(3x^{2}+2)dx
limit as x approaches 1/3 x of sin(x)	\lim\:_{x\to\:\frac{1}{3}x}(\sin(x))
y^'=e^{2x-y}	y^{\prime\:}=e^{2x-y}
taylor 2x^2+2x	taylor\:2x^{2}+2x
tangent of f(x)= x/(x^2+81),\at x=0	tangent\:f(x)=\frac{x}{x^{2}+81},\at\:x=0
integral from-pi to pi of \|x\|cos(nx)	\int\:_{-π}^{π}\left\|x\right\|\cos(nx)dx
integral from 0 to 1 of (x^4+4)/x	\int\:_{0}^{1}\frac{x^{4}+4}{x}dx
limit as x approaches 4 of 1/((4-x)^2)	\lim\:_{x\to\:4}(\frac{1}{(4-x)^{2}})
derivative of a+bxcos(3x+cxsin(3x))	\frac{d}{dx}(a+bx\cos(3x)+cx\sin(3x))
(\partial)/(\partial x)(2xy-2y)	\frac{\partial\:}{\partial\:x}(2xy-2y)
(\partial)/(\partial y)(1/(1+x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{1}{1+x^{2}+y^{2}})
derivative of x^2sqrt(x^3+a^3)	\frac{d}{dx}(x^{2}\sqrt{x^{3}+a^{3}})
integral of (3x^3+3x+2)/(x^3+x)	\int\:\frac{3x^{3}+3x+2}{x^{3}+x}dx
tangent of f(x)= 1/(x^4),\at x=3	tangent\:f(x)=\frac{1}{x^{4}},\at\:x=3
(\partial)/(\partial z)(xe^z)	\frac{\partial\:}{\partial\:z}(xe^{z})
derivative of 1/(x+9)	derivative\:\frac{1}{x+9}
integral of (e^{x/2})/x	\int\:\frac{e^{\frac{x}{2}}}{x}dx
integral of 7x^3+4x^2	\int\:7x^{3}+4x^{2}dx
tangent of 3/(2sqrt(x))	tangent\:\frac{3}{2\sqrt{x}}
derivative of ln((x-3^2))	\frac{d}{dx}(\ln((x-3)^{2}))
taylor sqrt(x)	taylor\:\sqrt{x}
derivative of 1/(x^7+1/(x^8))	\frac{d}{dx}(\frac{1}{x^{7}}+\frac{1}{x^{8}})
sum from n=1 to infinity of ne^{7n}	\sum\:_{n=1}^{\infty\:}ne^{7n}
derivative of x/((1+x^2))	derivative\:\frac{x}{(1+x^{2})}
limit as x approaches-4 of (x^2+2)/(x+5)	\lim\:_{x\to\:-4}(\frac{x^{2}+2}{x+5})
(dy)/(dx)=xy^2	\frac{dy}{dx}=xy^{2}
(\partial)/(\partial y)(x*y+y^2)	\frac{\partial\:}{\partial\:y}(x\cdot\:y+y^{2})
integral of cos(x)-1	\int\:\cos(x)-1dx
tangent of f(x)=2xe^x,\at x=0	tangent\:f(x)=2xe^{x},\at\:x=0
(\partial)/(\partial x)(4ln(xy)+3ln(yz)+ln(xz))	\frac{\partial\:}{\partial\:x}(4\ln(xy)+3\ln(yz)+\ln(xz))
area x=y^2-4y,x=y-y^2	area\:x=y^{2}-4y,x=y-y^{2}
2y^{''}-15y^'-8y=0	2y^{\prime\:\prime\:}-15y^{\prime\:}-8y=0
integral from-1 to 1 of x-sqrt(1-x^2)	\int\:_{-1}^{1}x-\sqrt{1-x^{2}}dx
derivative of y=(x^6-10)sqrt(x)	derivative\:y=(x^{6}-10)\sqrt{x}
integral of sin^5(x)cos^8(x)	\int\:\sin^{5}(x)\cos^{8}(x)dx
sum from n=3 to infinity of 1/(n^2-1)	\sum\:_{n=3}^{\infty\:}\frac{1}{n^{2}-1}
inverse oflaplace s/((s^2+9)^2)	inverselaplace\:\frac{s}{(s^{2}+9)^{2}}
tangent of y= 1/(sqrt(4-x))	tangent\:y=\frac{1}{\sqrt{4-x}}
integral of ((4x-7))/(x^2-6x+13)	\int\:\frac{(4x-7)}{x^{2}-6x+13}dx
derivative of-7/(x^2)	derivative\:-\frac{7}{x^{2}}
(x^2+4)dy=(2x-8xy)dx	(x^{2}+4)dy=(2x-8xy)dx
integral of-2/(pin)cos((pin)/2 x)	\int\:-\frac{2}{πn}\cos(\frac{πn}{2}x)dx
(dy)/(dx)=(7x^2)/(5y^2)	\frac{dy}{dx}=\frac{7x^{2}}{5y^{2}}
derivative of f(x)=(((x+1))/((x-1)))^2	derivative\:f(x)=(\frac{(x+1)}{(x-1)})^{2}
integral of 7tan^2(x)sec(x)	\int\:7\tan^{2}(x)\sec(x)dx
limit as x approaches 0 of 2/(1+2^{1/x)}	\lim\:_{x\to\:0}(\frac{2}{1+2^{\frac{1}{x}}})

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