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Popular Calculus Problems

derivative of 2t^2-3t-1	derivative\:2t^{2}-3t-1
integral of 1/(x^2+2^2)	\int\:\frac{1}{x^{2}+2^{2}}dx
derivative of 1/((4x+1)^4)	derivative\:\frac{1}{(4x+1)^{4}}
limit as x approaches 3-of (x-2)/(x^2-9)	\lim\:_{x\to\:3-}(\frac{x-2}{x^{2}-9})
derivative of arccsc(-3x)	\frac{d}{dx}(\arccsc(-3x))
derivative of arctan(t/x)	\frac{d}{dx}(\arctan(\frac{t}{x}))
derivative of (2x-4/(3e^x))	\frac{d}{dx}(\frac{2x-4}{3e^{x}})
limit as x approaches 3 of 1/((x^2-9))	\lim\:_{x\to\:3}(\frac{1}{(x^{2}-9)})
integral of 2xe^{-2x^2}	\int\:2xe^{-2x^{2}}dx
derivative of f(x)=x^5*e^x	derivative\:f(x)=x^{5}\cdot\:e^{x}
sum from n=1 to infinity of ((x+3)^n)/n	\sum\:_{n=1}^{\infty\:}\frac{(x+3)^{n}}{n}
integral of 20+0.6sqrt(x)	\int\:20+0.6\sqrt{x}dx
derivative of (e/(16))^x	derivative\:(\frac{e}{16})^{x}
integral from 0 to 1/2 of y^2(8y)	\int\:_{0}^{\frac{1}{2}}y^{2}(8y)dy
tangent of y=(x^2-1)	tangent\:y=(x^{2}-1)
tangent of f(x)=5+4x^2-2x^3,\at x=a	tangent\:f(x)=5+4x^{2}-2x^{3},\at\:x=a
limit as x approaches infinity of-x+2	\lim\:_{x\to\:\infty\:}(-x+2)
integral from 0 to pi of 3sin^2(4x)	\int\:_{0}^{π}3\sin^{2}(4x)dx
integral of e^x	\int\:e^{x}dx
derivative of (1+sin(x)sin(x))	\frac{d}{dx}((1+\sin(x))\sin(x))
y^'=(x-1)e^x	y^{\prime\:}=(x-1)e^{x}
derivative of (0.3(9^x))/(x^3)	derivative\:\frac{0.3(9^{x})}{x^{3}}
integral of (cos(x)+1/2 x)	\int\:(\cos(x)+\frac{1}{2}x)dx
(dy}{dx}-y=\frac{e^x)/y	\frac{dy}{dx}-y=\frac{e^{x}}{y}
(\partial)/(\partial x)((x^2)^{-1/2})	\frac{\partial\:}{\partial\:x}((x^{2})^{-\frac{1}{2}})
derivative of u(x)=3x^2-x+6	derivative\:u(x)=3x^{2}-x+6
derivative of f(x)= 5/(\sqrt[4]{x)},x=2	derivative\:f(x)=\frac{5}{\sqrt[4]{x}},x=2
(d^2)/(dx^2)(3x^{-3}+5x^2)	\frac{d^{2}}{dx^{2}}(3x^{-3}+5x^{2})
integral of x/((2x+1)^3)	\int\:\frac{x}{(2x+1)^{3}}dx
(dx)/(x-x^2)=3dt	\frac{dx}{x-x^{2}}=3dt
(\partial)/(\partial y)(sqrt(14-x^2-4y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{14-x^{2}-4y^{2}})
limit as x approaches 2 of (x^2+1)/x	\lim\:_{x\to\:2}(\frac{x^{2}+1}{x})
derivative of e^4+ln(8)	\frac{d}{dx}(e^{4}+\ln(8))
integral of e^{3x+4}	\int\:e^{3x+4}dx
limit as x approaches 2-of-2	\lim\:_{x\to\:2-}(-2)
area y=sqrt(x)+3,y= 1/2 x+3	area\:y=\sqrt{x}+3,y=\frac{1}{2}x+3
(\partial)/(\partial x)(sqrt(5x^2+5y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{5x^{2}+5y^{2}})
(\partial)/(\partial x)(x*e^{x-y-z})	\frac{\partial\:}{\partial\:x}(x\cdot\:e^{x-y-z})
derivative of-2xy	derivative\:-2xy
derivative of (81)/(8(3x+2)^{5/2)}	derivative\:\frac{81}{8(3x+2)^{\frac{5}{2}}}
integral of 2x+4/(sqrt(x))	\int\:2x+\frac{4}{\sqrt{x}}dx
(\partial)/(\partial x)(5x+10y+10xy)	\frac{\partial\:}{\partial\:x}(5x+10y+10xy)
4t(dy)/(dt)+22y=0	4t\frac{dy}{dt}+22y=0
sum from n=1 to infinity of n/n	\sum\:_{n=1}^{\infty\:}\frac{n}{n}
derivative of sec(2x+tan(2x))	\frac{d}{dx}(\sec(2x)+\tan(2x))
integral of cos(8x)	\int\:\cos(8x)dx
f(x)=e^xsqrt(x)	f(x)=e^{x}\sqrt{x}
y^{''}-8y^'+16y=0,y(0)=3,y^'(0)=11	y^{\prime\:\prime\:}-8y^{\prime\:}+16y=0,y(0)=3,y^{\prime\:}(0)=11
integral of 5tan(2x)ln(cos(2x))	\int\:5\tan(2x)\ln(\cos(2x))dx
(\partial)/(\partial t)(zy^2(t+1))	\frac{\partial\:}{\partial\:t}(zy^{2}(t+1))
(dy)/(dx)=(xy^3)/(sqrt(1+x^2)),y(0)=-1	\frac{dy}{dx}=\frac{xy^{3}}{\sqrt{1+x^{2}}},y(0)=-1
integral of 7e^{-7x}sin(7x)	\int\:7e^{-7x}\sin(7x)dx
(dy}{dx}=\frac{2y)/x+x^2y^5	\frac{dy}{dx}=\frac{2y}{x}+x^{2}y^{5}
integral from 0 to 1 of 4e^{5sqrt(x)}	\int\:_{0}^{1}4e^{5\sqrt{x}}dx
integral of 2-4x	\int\:2-4xdx
(d^2)/(dx^2)(e^{9e^x})	\frac{d^{2}}{dx^{2}}(e^{9e^{x}})
derivative of f(x)= 5/(x+5)	derivative\:f(x)=\frac{5}{x+5}
integral of (sin(3x))/(cos^2(3x))	\int\:\frac{\sin(3x)}{\cos^{2}(3x)}dx
area 2x^2,2x+2	area\:2x^{2},2x+2
integral of e^{x^2-x}	\int\:e^{x^{2}-x}dx
(\partial)/(\partial x)(arccos(x/(sqrt(x^2+y^2))))	\frac{\partial\:}{\partial\:x}(\arccos(\frac{x}{\sqrt{x^{2}+y^{2}}}))
7y^'=y^2	7y^{\prime\:}=y^{2}
derivative of f(x)=xe^{3x^2+1}	derivative\:f(x)=xe^{3x^{2}+1}
integral of 1/((y+1)(y-2))	\int\:\frac{1}{(y+1)(y-2)}dy
tangent of f(x)=x^2+sin(x)	tangent\:f(x)=x^{2}+\sin(x)
integral of x^2-3x	\int\:x^{2}-3xdx
(\partial)/(\partial x)(x^2y+y)	\frac{\partial\:}{\partial\:x}(x^{2}y+y)
derivative of log_{e}(x+1)	\frac{d}{dx}(\log_{e}(x+1))
integral of 1/(cos(θ)-1)	\int\:\frac{1}{\cos(θ)-1}dθ
y^{'''}-9y^{''}+15y^'+25y=0	y^{\prime\:\prime\:\prime\:}-9y^{\prime\:\prime\:}+15y^{\prime\:}+25y=0
(\partial)/(\partial x)(x/v)	\frac{\partial\:}{\partial\:x}(\frac{x}{v})
limit as x approaches 8+of (\|x-8\|)/(x-8)	\lim\:_{x\to\:8+}(\frac{\left\|x-8\right\|}{x-8})
derivative of (5x^3-7/x)	\frac{d}{dx}(\frac{5x^{3}-7}{x})
f(x)=10cos(30x-7)	f(x)=10\cos(30x-7)
integral of (-2x)/(1+x^2)	\int\:\frac{-2x}{1+x^{2}}dx
(\partial)/(\partial x)(e^{-8x})	\frac{\partial\:}{\partial\:x}(e^{-8x})
d/(dy)(cos(2y))	\frac{d}{dy}(\cos(2y))
limit as x approaches 0-of 5x^3-7x^2+2^x-2	\lim\:_{x\to\:0-}(5x^{3}-7x^{2}+2^{x}-2)
integral of 1/(sqrt(t^2-6t+34))	\int\:\frac{1}{\sqrt{t^{2}-6t+34}}dt
tangent of f(x)=8(x-1/x)^2	tangent\:f(x)=8(x-\frac{1}{x})^{2}
integral of sin(x^3)	\int\:\sin(x^{3})dx
derivative of 6sin(6x)	\frac{d}{dx}(6\sin(6x))
integral of x/(x-7)	\int\:\frac{x}{x-7}dx
integral of 5sin(6pi)t	\int\:5\sin(6π)tdt
integral of (3x^2-2/(x^3)+\sqrt[3]{x}-8)	\int\:(3x^{2}-\frac{2}{x^{3}}+\sqrt[3]{x}-8)dx
derivative of (2x)/(x^2+1)	derivative\:\frac{2x}{x^{2}+1}
x^{''}+3x^'+2x=e^{-t}	x^{\prime\:\prime\:}+3x^{\prime\:}+2x=e^{-t}
tangent of sqrt((3x+25))	tangent\:\sqrt{(3x+25)}
(\partial)/(\partial x)(e^{2x}cos(y))	\frac{\partial\:}{\partial\:x}(e^{2x}\cos(y))
limit as x approaches-2 of 3x+4	\lim\:_{x\to\:-2}(3x+4)
integral of xe^{5x}	\int\:xe^{5x}dx
limit as h approaches 0 of 1/(h^2)	\lim\:_{h\to\:0}(\frac{1}{h^{2}})
integral of xn(x)	\int\:xn(x)dx
integral of sec^{13}(x)	\int\:\sec^{13}(x)dx
f(x)=sinh(2x)	f(x)=\sinh(2x)
integral from 0 to ln(2) of e^{x+2y}	\int\:_{0}^{\ln(2)}e^{x+2y}dx
(\partial)/(\partial x)(2x*e^{xy})	\frac{\partial\:}{\partial\:x}(2x\cdot\:e^{xy})
(\partial)/(\partial x)(x^2z+3z^2x+6(x+z))	\frac{\partial\:}{\partial\:x}(x^{2}z+3z^{2}x+6(x+z))
derivative of 2x^6-8x^5+10x^4-10x^2+8x-2	\frac{d}{dx}(2x^{6}-8x^{5}+10x^{4}-10x^{2}+8x-2)
integral of (x-4)/(x^2+2x-15)	\int\:\frac{x-4}{x^{2}+2x-15}dx

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