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Popular Calculus Problems

derivative of 3sin^5(x)	\frac{d}{dx}(3\sin^{5}(x))
derivative of (x+1(x+2))	\frac{d}{dx}((x+1)(x+2))
(\partial)/(\partial x)(y^2-2ycos(x))	\frac{\partial\:}{\partial\:x}(y^{2}-2y\cos(x))
d/(dt)({v}(t))	\frac{d}{dt}({v}(t))
derivative of ({f}(x)/({g)(x)})	\frac{d}{dx}(\frac{{f}(x)}{{g}(x)})
y^{''}+9y=2cos(3x)	y^{\prime\:\prime\:}+9y=2\cos(3x)
derivative of 1/4 e^{3x}	derivative\:\frac{1}{4}e^{3x}
limit as x approaches 1-of sqrt(x^2-1)	\lim\:_{x\to\:1-}(\sqrt{x^{2}-1})
(\partial)/(\partial x)(9x^{5y})	\frac{\partial\:}{\partial\:x}(9x^{5y})
(d^8)/(dx^8)(sqrt(1-x^2))	\frac{d^{8}}{dx^{8}}(\sqrt{1-x^{2}})
inverse oflaplace (3s)/((s^2+1))	inverselaplace\:\frac{3s}{(s^{2}+1)}
extreme f(x)=rx+n	extreme\:f(x)=rx+n
(\partial)/(\partial t)(t-s)	\frac{\partial\:}{\partial\:t}(t-s)
derivative of-2x^4+5x^2-3	derivative\:-2x^{4}+5x^{2}-3
derivative of f(x)=e^{4tsin(2t)}	derivative\:f(x)=e^{4t\sin(2t)}
y^'=e^{(t+y)},y(0)=0	y^{\prime\:}=e^{(t+y)},y(0)=0
x^2((dy)/(dx))+4xy-y^3=0	x^{2}(\frac{dy}{dx})+4xy-y^{3}=0
limit as x approaches 2 of (3x-1)^{x^2-3x+4}	\lim\:_{x\to\:2}((3x-1)^{x^{2}-3x+4})
(\partial)/(\partial y)(ln(x/y))	\frac{\partial\:}{\partial\:y}(\ln(\frac{x}{y}))
limit as x approaches 0 of 2/x-2/x	\lim\:_{x\to\:0}(\frac{2}{x}-\frac{2}{x})
area 2/x , 2/(x^2),x=4	area\:\frac{2}{x},\frac{2}{x^{2}},x=4
derivative of f(x)=6sec(x)-5x	derivative\:f(x)=6\sec(x)-5x
derivative of sqrt(sec(5x^2))	\frac{d}{dx}(\sqrt{\sec(5)x^{2}})
sum from n=1 to infinity of 7/(n^5)	\sum\:_{n=1}^{\infty\:}\frac{7}{n^{5}}
derivative of y=5x^2	derivative\:y=5x^{2}
derivative of (4e^x/x)	\frac{d}{dx}(\frac{4e^{x}}{x})
derivative of f(x)=x^{2cos(x)}	derivative\:f(x)=x^{2\cos(x)}
(\partial)/(\partial y)(4x^{2y})	\frac{\partial\:}{\partial\:y}(4x^{2y})
(d^2y)/(dx^2)=x	\frac{d^{2}y}{dx^{2}}=x
tangent of f(x)= x/(x^2+1)	tangent\:f(x)=\frac{x}{x^{2}+1}
derivative of (cot(x)/(1+cot(x)))	\frac{d}{dx}(\frac{\cot(x)}{1+\cot(x)})
implicit (dy)/(dx),y-5xy^3+8=5sin(y^3+2x^2)	implicit\:\frac{dy}{dx},y-5xy^{3}+8=5\sin(y^{3}+2x^{2})
(\partial)/(\partial x)(x(y+1))	\frac{\partial\:}{\partial\:x}(x(y+1))
integral from 0 to 2pi of sin^4(x)	\int\:_{0}^{2π}\sin^{4}(x)dx
derivative of sin(9x+(sin(9x))^2)	\frac{d}{dx}(\sin(9x)+(\sin(9x))^{2})
derivative of f(2x)=5x-3	derivative\:f(2x)=5x-3
(\partial)/(\partial x)(x+sqrt(y))	\frac{\partial\:}{\partial\:x}(x+\sqrt{y})
(t+y+1)dt-dy=0	(t+y+1)dt-dy=0
derivative of f(x)=2x-4	derivative\:f(x)=2x-4
derivative of ((x+1/(x-1))^4)	\frac{d}{dx}((\frac{x+1}{x-1})^{4})
integral of ln(x)-9x^2	\int\:\ln(x)-9x^{2}dx
laplacetransform 3sin^2(t)	laplacetransform\:3\sin^{2}(t)
(\partial)/(\partial x)(y^2+6x-x^2y+36)	\frac{\partial\:}{\partial\:x}(y^{2}+6x-x^{2}y+36)
integral of sqrt(2t)	\int\:\sqrt{2t}dt
integral of (4x+4)sqrt(2x^2+4x)	\int\:(4x+4)\sqrt{2x^{2}+4x}dx
integral of 50x	\int\:50xdx
area sqrt(x-1),x-1	area\:\sqrt{x-1},x-1
integral from 0 to pi of 3e^xsin(x)	\int\:_{0}^{π}3e^{x}\sin(x)dx
derivative of 1/(sqrt(9-x^2))	\frac{d}{dx}(\frac{1}{\sqrt{9-x^{2}}})
inverse oflaplace 1/((s+1)^2*(s-1))	inverselaplace\:\frac{1}{(s+1)^{2}\cdot\:(s-1)}
limit as h approaches 0 of (8^h-1)/h	\lim\:_{h\to\:0}(\frac{8^{h}-1}{h})
derivative of f(x)=(x^2+2x-3)/((x+1)^2)	derivative\:f(x)=\frac{x^{2}+2x-3}{(x+1)^{2}}
integral from-infinity to 0 of 1/(6-4x)	\int\:_{-\infty\:}^{0}\frac{1}{6-4x}dx
y^{''}+7y^'+14y=1096e^{2t}cos(8t)	y^{\prime\:\prime\:}+7y^{\prime\:}+14y=1096e^{2t}\cos(8t)
limit as x approaches 4-of x/(x^2-16)	\lim\:_{x\to\:4-}(\frac{x}{x^{2}-16})
(dy)/(dx)= x/(25y),y(5)=1	\frac{dy}{dx}=\frac{x}{25y},y(5)=1
laplacetransform cos(t)*e^t	laplacetransform\:\cos(t)\cdot\:e^{t}
integral of (tan^3(x))/(sec^2(x)-1)	\int\:\frac{\tan^{3}(x)}{\sec^{2}(x)-1}dx
derivative of y=ln(xln(x))	derivative\:y=\ln(x\ln(x))
integral of sec^5(t)	\int\:\sec^{5}(t)dt
(\partial ^2)/(\partial x^2)(x^2-e^{y^2})	\frac{\partial\:^{2}}{\partial\:x^{2}}(x^{2}-e^{y^{2}})
derivative of ln\|sec(θ)+tan(θ)\|	derivative\:\ln\left\|\sec(θ)+\tan(θ)\right\|
integral from 0 to 1 of (x^4+2)/x	\int\:_{0}^{1}\frac{x^{4}+2}{x}dx
derivative of (sqrt(s)-1)/(sqrt(s)+1)	derivative\:\frac{\sqrt{s}-1}{\sqrt{s}+1}
(\partial)/(\partial x)(e^ye^x)	\frac{\partial\:}{\partial\:x}(e^{y}e^{x})
(\partial)/(\partial x)(ye^{-2x})	\frac{\partial\:}{\partial\:x}(ye^{-2x})
laplacetransform-2t	laplacetransform\:-2t
(\partial)/(\partial x)(ln((x+y)/(x-y)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{x+y}{x-y}))
integral from 0 to 1 of v^2cos(v^3)	\int\:_{0}^{1}v^{2}\cos(v^{3})dv
derivative of (d/(dx(x^3))^2)	\frac{d}{dx}((\frac{d}{dx}(x^{3}))^{2})
derivative of sqrt(3x^2-4x+2)	\frac{d}{dx}(\sqrt{3x^{2}-4x+2})
(dy)/(dx)+y=e^{6x}	\frac{dy}{dx}+y=e^{6x}
derivative of cos^2(sin(2x))	\frac{d}{dx}(\cos^{2}(\sin(2x)))
derivative of (x^2+1^{ln(x)})	\frac{d}{dx}((x^{2}+1)^{\ln(x)})
sum from i=1 to infinity of 4(2)^{i-1}	\sum\:_{i=1}^{\infty\:}4(2)^{i-1}
integral of (ln(x)-2)/(xln(x)(ln(x)-1))	\int\:\frac{\ln(x)-2}{x\ln(x)(\ln(x)-1)}dx
integral of sin(x)ln(x)cos(x)	\int\:\sin(x)\ln(x)\cos(x)dx
laplacetransform e^{mt}	laplacetransform\:e^{mt}
integral of x/(sqrt(5+4x))	\int\:\frac{x}{\sqrt{5+4x}}dx
integral of x(x^2+3)^5	\int\:x(x^{2}+3)^{5}dx
derivative of 3x^5-4x^4+9x-6	\frac{d}{dx}(3x^{5}-4x^{4}+9x-6)
integral of (sin(x))/2	\int\:\frac{\sin(x)}{2}dx
derivative of sin(y-ysin(x))	\frac{d}{dx}(\sin(y)-y\sin(x))
integral of sec^5(2x)tan(2x)	\int\:\sec^{5}(2x)\tan(2x)dx
limit as x approaches 1+of 6/(x-1)	\lim\:_{x\to\:1+}(\frac{6}{x-1})
integral of 1/9 e^{3x}	\int\:\frac{1}{9}e^{3x}dx
derivative of sqrt(26x-x^2)	\frac{d}{dx}(\sqrt{26x-x^{2}})
derivative of f(x)=((e^{4x})/(x^6))^3	derivative\:f(x)=(\frac{e^{4x}}{x^{6}})^{3}
integral of 3xcos(2x)	\int\:3x\cos(2x)dx
integral of \sqrt[3]{5-3x^2}(-6x)	\int\:\sqrt[3]{5-3x^{2}}(-6x)dx
integral from 0 to xb of ((1-0.25x)^3)/((1-1/2 x)(1-x)^2)	\int\:_{0}^{xb}\frac{(1-0.25x)^{3}}{(1-\frac{1}{2}x)(1-x)^{2}}dx
integral of (4x^3-\sqrt[4]{x})/(2x)	\int\:\frac{4x^{3}-\sqrt[4]{x}}{2x}dx
limit as x approaches-2 of x^2+2t-1	\lim\:_{x\to\:-2}(x^{2}+2t-1)
integral of ((x+1)/x)^2	\int\:(\frac{x+1}{x})^{2}dx
derivative of f(x)=ln((20+2x)^4)	derivative\:f(x)=\ln((20+2x)^{4})
y^'=0.05y-48000	y^{\prime\:}=0.05y-48000
integral of (cos(pi/(x^{12)}))/(x^{13)}	\int\:\frac{\cos(\frac{π}{x^{12}})}{x^{13}}dx
derivative of sqrt(4(x+2)^3)	derivative\:\sqrt{4(x+2)^{3}}
integral of a/(s^2-a^2)	\int\:\frac{a}{s^{2}-a^{2}}ds
derivative of Insqrt(x)	\frac{d}{dx}(In\sqrt{x})

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