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Popular Calculus Problems

derivative of 1/((1+x^2)^2)	derivative\:\frac{1}{(1+x^{2})^{2}}
tangent of (sqrt(x)+1)/(sqrt(x)+7)	tangent\:\frac{\sqrt{x}+1}{\sqrt{x}+7}
(2xy^2+2y)+(2x^2y+2x)y^'=0	(2xy^{2}+2y)+(2x^{2}y+2x)y^{\prime\:}=0
derivative of e^{3x}cos(6x)	derivative\:e^{3x}\cos(6x)
5xy^'-2y=9x^2	5xy^{\prime\:}-2y=9x^{2}
derivative of (x^3/3-(x^2)/2-6x)	\frac{d}{dx}(\frac{x^{3}}{3}-\frac{x^{2}}{2}-6x)
derivative of e^xx^5+10e^xx^4+20e^xx^3	\frac{d}{dx}(e^{x}x^{5}+10e^{x}x^{4}+20e^{x}x^{3})
integral of 9sin^2(x)cos(x)	\int\:9\sin^{2}(x)\cos(x)dx
f(x)=4x+5	f(x)=4x+5
integral of (x^3+cos(2x))	\int\:(x^{3}+\cos(2x))dx
f(θ)=2sin(θ)	f(θ)=2\sin(θ)
integral from 1 to e of 2xln(x)	\int\:_{1}^{e}2x\ln(x)dx
integral of (2sin(ln(x)))/x	\int\:\frac{2\sin(\ln(x))}{x}dx
tangent of y^3-xy^2+x^3=5,(1,2)	tangent\:y^{3}-xy^{2}+x^{3}=5,(1,2)
integral of xcosh(x)	\int\:x\cosh(x)dx
derivative of f(x)=x^3cos(x)	derivative\:f(x)=x^{3}\cos(x)
derivative of (sin(x)^{1/3})	\frac{d}{dx}((\sin(x))^{\frac{1}{3}})
laplacetransform 24e^{-7t}-5e^{-23t}	laplacetransform\:24e^{-7t}-5e^{-23t}
(dy)/(dt)-2y=4-t	\frac{dy}{dt}-2y=4-t
derivative of-1/(4(1+x^{3/2)})	\frac{d}{dx}(-\frac{1}{4(1+x)^{\frac{3}{2}}})
(\partial)/(\partial y)(xyz+xy^3+yz^3+zx^3)	\frac{\partial\:}{\partial\:y}(xyz+xy^{3}+yz^{3}+zx^{3})
sum from n=1 to infinity of (x-4)^n	\sum\:_{n=1}^{\infty\:}(x-4)^{n}
derivative of ln(xsqrt(x^2-9))	\frac{d}{dx}(\ln(x\sqrt{x^{2}-9}))
limit as x approaches infinity of 15	\lim\:_{x\to\:\infty\:}(15)
derivative of f(x)= x/(sqrt(x)+9)	derivative\:f(x)=\frac{x}{\sqrt{x}+9}
integral of x^3(2x^2-3)	\int\:x^{3}(2x^{2}-3)dx
(\partial)/(\partial x)(4xy(-12-x-y))	\frac{\partial\:}{\partial\:x}(4xy(-12-x-y))
inverse oflaplace 1/(s(s-1))	inverselaplace\:\frac{1}{s(s-1)}
limit as x approaches 3 of (1-3x)^{1/x}	\lim\:_{x\to\:3}((1-3x)^{\frac{1}{x}})
integral of tan(2x)	\int\:\tan(2x)dx
(\partial)/(\partial z)(6y(z+1)^4)	\frac{\partial\:}{\partial\:z}(6y(z+1)^{4})
integral of (1-2x)	\int\:(1-2x)dx
limit as x approaches-infinity of 1x	\lim\:_{x\to\:-\infty\:}(1x)
area y=x^2+1,y=5	area\:y=x^{2}+1,y=5
tangent of f(x)=7x^2-x^3,(1,6)	tangent\:f(x)=7x^{2}-x^{3},(1,6)
integral of 18x^2-14x+9	\int\:18x^{2}-14x+9dx
tangent of x+2/x	tangent\:x+\frac{2}{x}
t^2y^{''}-2ty^'+2y=3t^2	t^{2}y^{\prime\:\prime\:}-2ty^{\prime\:}+2y=3t^{2}
integral from 1 to sqrt(3 of)arctan(1/x)	\int\:_{1}^{\sqrt{3}}\arctan(\frac{1}{x})dx
derivative of f(x)\sqrt[5]{x}	derivative\:f(x)\sqrt[5]{x}
tangent of y=(x^2)/(x+2),(2,1)	tangent\:y=\frac{x^{2}}{x+2},(2,1)
derivative of x-2x^2+1	\frac{d}{dx}(x-2x^{2}+1)
limit as x approaches-2 of ((x^2-3x-10))/((x^2+5x+6))	\lim\:_{x\to\:-2}(\frac{(x^{2}-3x-10)}{(x^{2}+5x+6)})
derivative of 2(6x^2-7x(12x-7))	\frac{d}{dx}(2(6x^{2}-7x)(12x-7))
integral of e^{-sx}(2-x)	\int\:e^{-sx}(2-x)dx
limit as x approaches 1 of 1/(x^3-1)	\lim\:_{x\to\:1}(\frac{1}{x^{3}-1})
derivative of 3-3cos(x)	\frac{d}{dx}(3-3\cos(x))
(dy)/(dx)=(x-4)e^{-2y}	\frac{dy}{dx}=(x-4)e^{-2y}
y^'=6x^2*sqrt(y)	y^{\prime\:}=6x^{2}\cdot\:\sqrt{y}
integral of 4e^{-7x}	\int\:4e^{-7x}dx
derivative of f(x)=(x^3+5)/x	derivative\:f(x)=\frac{x^{3}+5}{x}
laplacetransform e^{7t}	laplacetransform\:e^{7t}
integral from 1/2 to 1 of (x^{-3}-21)	\int\:_{\frac{1}{2}}^{1}(x^{-3}-21)dx
sum from n=0 to infinity of 1/(2+3^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{2+3^{n}}
derivative of 2cos(x+cos(2x))	\frac{d}{dx}(2\cos(x)+\cos(2x))
tangent of f(x)=(8x^2)/(ln(x)+2),\at x=1	tangent\:f(x)=\frac{8x^{2}}{\ln(x)+2},\at\:x=1
(\partial)/(\partial y)(xcos(x)cos(y))	\frac{\partial\:}{\partial\:y}(x\cos(x)\cos(y))
integral of x/((x^2-3)^5)	\int\:\frac{x}{(x^{2}-3)^{5}}dx
derivative of 14x^{-3}+x^2+14	derivative\:14x^{-3}+x^{2}+14
derivative of (2x+1^3(x-3)^4)	\frac{d}{dx}((2x+1)^{3}(x-3)^{4})
integral of (tan(ln(x^2)))/(4x)	\int\:\frac{\tan(\ln(x^{2}))}{4x}dx
derivative of 7e^t	derivative\:7e^{t}
derivative of 3xsqrt(4x^2+4)	derivative\:3x\sqrt{4x^{2}+4}
integral of xsqrt(25+x^2)	\int\:x\sqrt{25+x^{2}}dx
(\partial)/(\partial x)(sin(z)cos(xy))	\frac{\partial\:}{\partial\:x}(\sin(z)\cdot\:\cos(x\cdot\:y))
(2+x)y^'=5y	(2+x)y^{\prime\:}=5y
(\partial)/(\partial x)(x+2/y)	\frac{\partial\:}{\partial\:x}(x+\frac{2}{y})
taylor 1/(1-x+\frac{x^2){2}},0	taylor\:\frac{1}{1-x+\frac{x^{2}}{2}},0
derivative of (4x^2tan(x)/(sec(x)))	\frac{d}{dx}(\frac{4x^{2}\tan(x)}{\sec(x)})
derivative of x^8(x-1^7)	\frac{d}{dx}(x^{8}(x-1)^{7})
integral of (2x-4)	\int\:(2x-4)dx
integral of (-3/7 x^5+1/5 x^3-7/4 x^2)	\int\:(-\frac{3}{7}x^{5}+\frac{1}{5}x^{3}-\frac{7}{4}x^{2})dx
integral of (3x)/(x^2+2x-8)	\int\:\frac{3x}{x^{2}+2x-8}dx
derivative of 6x+3	\frac{d}{dx}(6x+3)
limit as x approaches 3 of (x^2+1)/(x+3)	\lim\:_{x\to\:3}(\frac{x^{2}+1}{x+3})
y^'=sqrt(y),y(1)=1	y^{\prime\:}=\sqrt{y},y(1)=1
integral of x/(sqrt(1-x^2))	\int\:\frac{x}{\sqrt{1-x^{2}}}dx
derivative of arccos(4x)	\frac{d}{dx}(\arccos(4x))
(\partial)/(\partial y)(ln\|x+y\|)	\frac{\partial\:}{\partial\:y}(\ln\left\|x+y\right\|)
(dy)/(dx)=e^{3y+10x}	\frac{dy}{dx}=e^{3y+10x}
derivative of sin(x(1-cos(x)))	\frac{d}{dx}(\sin(x)(1-\cos(x)))
sum from n=0 to infinity of 1/(2-e^{-n)}	\sum\:_{n=0}^{\infty\:}\frac{1}{2-e^{-n}}
derivative of f(x)=-10xsin(5x^2+5)	derivative\:f(x)=-10x\sin(5x^{2}+5)
derivative of (4-x^{2/3}^{2/3})	\frac{d}{dx}((4-x^{\frac{2}{3}})^{\frac{2}{3}})
derivative of 1/(10x^{9/10})	\frac{d}{dx}(\frac{1}{10x^{\frac{9}{10}}})
integral of (x-11)/(x^2+6x+25)	\int\:\frac{x-11}{x^{2}+6x+25}dx
derivative of f(x)=x(7^{-3x})	derivative\:f(x)=x(7^{-3x})
integral of (x^2-7x+12)/(x-3)	\int\:\frac{x^{2}-7x+12}{x-3}dx
derivative of y=(3x-9)/(2x+8)	derivative\:y=\frac{3x-9}{2x+8}
derivative of (4+ln(2x)/(2020+x))	\frac{d}{dx}(\frac{4+\ln(2x)}{2020+x})
taylor e^{4x},3	taylor\:e^{4x},3
derivative of 7arctan(x-sqrt(1+x^2))	derivative\:7\arctan(x-\sqrt{1+x^{2}})
laplacetransform 8e^{-6t}cos(4t+30)	laplacetransform\:8e^{-6t}\cos(4t+30)
integral from-infinity to 0 of 1/(4-10x)	\int\:_{-\infty\:}^{0}\frac{1}{4-10x}dx
tangent of f(x)=-2x^3,\at x=1	tangent\:f(x)=-2x^{3},\at\:x=1
integral of xsin(3x-2)	\int\:x\sin(3x-2)dx
laplacetransform-cos(2t)	laplacetransform\:-\cos(2t)
integral of 21xsec^2(x)	\int\:21x\sec^{2}(x)dx
integral of 1/(xln(x)ln(ln(x)))	\int\:\frac{1}{x\ln(x)\ln(\ln(x))}dx
derivative of f(x)=11^x	derivative\:f(x)=11^{x}

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