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Popular Calculus Problems

derivative of f(x)=5x^2cos(x)+4x	derivative\:f(x)=5x^{2}\cos(x)+4x
integral from 1 to-1 of 3e^x	\int\:_{1}^{-1}3e^{x}dx
t^2y^{''}+2ty^'-12y=0	t^{2}y^{\prime\:\prime\:}+2ty^{\prime\:}-12y=0
derivative of f(x)=9x^{7/5}-5x^2+10^4	derivative\:f(x)=9x^{\frac{7}{5}}-5x^{2}+10^{4}
derivative of 3x+sin(5x)	derivative\:3x+\sin(5x)
derivative of y= x/(4x+7)	derivative\:y=\frac{x}{4x+7}
f(x)=ln(cos(x))	f(x)=\ln(\cos(x))
derivative of 9e^{sqrt(x)}	\frac{d}{dx}(9e^{\sqrt{x}})
limit as x approaches 0 of (2^x-5^x)/x	\lim\:_{x\to\:0}(\frac{2^{x}-5^{x}}{x})
derivative of 2x^3-3x^2	\frac{d}{dx}(2x^{3}-3x^{2})
integral of (9/x+x/9)	\int\:(\frac{9}{x}+\frac{x}{9})dx
derivative of y=-2x+2	derivative\:y=-2x+2
integral of (-20x^3-6x^{-3})	\int\:(-20x^{3}-6x^{-3})dx
(\partial)/(\partial x)((7y-7x)/(y^2+2x^2))	\frac{\partial\:}{\partial\:x}(\frac{7y-7x}{y^{2}+2x^{2}})
(x^2-2x-2sin(x-2))^'	(x^{2}-2x-2\sin(x-2))^{\prime\:}
limit as x approaches 2 of 4ln(2)	\lim\:_{x\to\:2}(4\ln(2))
sum from n=1 to infinity of (n!)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{n!}{n!}
integral of xcos(nxpi)	\int\:x\cos(nxπ)dx
integral of 1/(9e^{-8x)+e^{8x}}	\int\:\frac{1}{9e^{-8x}+e^{8x}}dx
derivative of f(x)=x^2sqrt(x-5x)	derivative\:f(x)=x^{2}\sqrt{x-5x}
derivative of (1-5x/(3+x))	\frac{d}{dx}(\frac{1-5x}{3+x})
(\partial)/(\partial x)(xarctan(y/z))	\frac{\partial\:}{\partial\:x}(x\arctan(\frac{y}{z}))
extreme f(r)=e^r+x^e	extreme\:f(r)=e^{r}+x^{e}
factor 0.1x^3-0.1x^2+50x	factor\:0.1x^{3}-0.1x^{2}+50x
d/(dy)(e^{x+y})	\frac{d}{dy}(e^{x+y})
f(x)= x/(3x-4ln(x))	f(x)=\frac{x}{3x-4\ln(x)}
limit as x approaches 2 of (x^2-9)/(x-3)	\lim\:_{x\to\:2}(\frac{x^{2}-9}{x-3})
tangent of p(θ)=sqrt(3θ)	tangent\:p(θ)=\sqrt{3θ}
xy^'=(y^2)/x+y	xy^{\prime\:}=\frac{y^{2}}{x}+y
y^'=1+(y/x)	y^{\prime\:}=1+(\frac{y}{x})
derivative of f(x)=sqrt(1+x^{256)}-1	derivative\:f(x)=\sqrt{1+x^{256}}-1
derivative of 2xsqrt(36-x^2)	\frac{d}{dx}(2x\sqrt{36-x^{2}})
xy^'+3y^'-(x+3)sin(x)+y=0	xy^{\prime\:}+3y^{\prime\:}-(x+3)\sin(x)+y=0
(\partial)/(\partial y)(x^2y-x-xy^2+y)	\frac{\partial\:}{\partial\:y}(x^{2}y-x-xy^{2}+y)
derivative of 18^x	\frac{d}{dx}(18^{x})
limit as x approaches 0 of cos(19x)	\lim\:_{x\to\:0}(\cos(19x))
(\partial)/(\partial x)(ln(x^3y+2z))	\frac{\partial\:}{\partial\:x}(\ln(x^{3}y+2z))
integral of sin^3(3x)cos(3x)	\int\:\sin^{3}(3x)\cos(3x)dx
limit as x approaches 0 of x^2tan(x)	\lim\:_{x\to\:0}(x^{2}\tan(x))
derivative of (8x)/(9-tan(x))	derivative\:\frac{8x}{9-\tan(x)}
tangent of sqrt(x+16),\at x=1	tangent\:\sqrt{x+16},\at\:x=1
limit as x approaches 7 of ln(x-7)	\lim\:_{x\to\:7}(\ln(x-7))
derivative of y=e^{3x}cos(6x)	derivative\:y=e^{3x}\cos(6x)
taylor 1/(1+x^2),1	taylor\:\frac{1}{1+x^{2}},1
tangent of 4/(5x+1)	tangent\:\frac{4}{5x+1}
(\partial)/(\partial x)(x/(sqrt(x^2+1)))	\frac{\partial\:}{\partial\:x}(\frac{x}{\sqrt{x^{2}+1}})
(dy)/(dt)= y/(t+1)+4t^2+4t,y(1)=-5	\frac{dy}{dt}=\frac{y}{t+1}+4t^{2}+4t,y(1)=-5
limit as x approaches 0 of 1/x-3	\lim\:_{x\to\:0}(\frac{1}{x}-3)
f(y)=(y-1)/(y^2-y+1)	f(y)=\frac{y-1}{y^{2}-y+1}
integral of (x+1)sqrt(4x+5)	\int\:(x+1)\sqrt{4x+5}dx
(\partial)/(\partial x)(sin(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\sin(x^{2}+y^{2}))
integral of cos(15x)	\int\:\cos(15x)dx
derivative of ln(1/(sqrt(1-x^2)))	\frac{d}{dx}(\ln(\frac{1}{\sqrt{1-x^{2}}}))
limit as x approaches-5-of 3	\lim\:_{x\to\:-5-}(3)
y^'=6-y	y^{\prime\:}=6-y
limit as x approaches 3-of (x^2)/(9-x^2)	\lim\:_{x\to\:3-}(\frac{x^{2}}{9-x^{2}})
integral from 0 to pi/4 of cos(2x)	\int\:_{0}^{\frac{π}{4}}\cos(2x)dx
derivative of y=(3x^3+7)^2	derivative\:y=(3x^{3}+7)^{2}
integral of (x+2)^{-1}	\int\:(x+2)^{-1}dx
(dy)/(dx)=7x^2*1/(5y^2)	\frac{dy}{dx}=7x^{2}\cdot\:\frac{1}{5y^{2}}
derivative of 7x^{1/3}	\frac{d}{dx}(7x^{\frac{1}{3}})
limit as x approaches 2 of 2/(x-2)	\lim\:_{x\to\:2}(\frac{2}{x-2})
derivative of-1/((1+x)^2)	derivative\:-\frac{1}{(1+x)^{2}}
derivative of 3x^2-x+12	\frac{d}{dx}(3x^{2}-x+12)
integral from 0 to 7 of (8x)/((x-8)^2)	\int\:_{0}^{7}\frac{8x}{(x-8)^{2}}dx
integral of t^{1/2}	\int\:t^{\frac{1}{2}}dt
derivative of y=arctan(x^2)	derivative\:y=\arctan(x^{2})
integral from-infinity to-1 of e^{-14t}	\int\:_{-\infty\:}^{-1}e^{-14t}dt
integral of 6x^2-5	\int\:6x^{2}-5dx
derivative of y= 7/x	derivative\:y=\frac{7}{x}
integral from 9 to 15 of 2cos((pix)/6)	\int\:_{9}^{15}2\cos(\frac{πx}{6})dx
(dt)/(dt)	\frac{dt}{dt}
area y=x^2-43,y=5-2x	area\:y=x^{2}-43,y=5-2x
(\partial)/(\partial x)(1+x^4+y^3)	\frac{\partial\:}{\partial\:x}(1+x^{4}+y^{3})
integral of 1/(x^4+16)	\int\:\frac{1}{x^{4}+16}dx
integral from 0 to pi/4 of 6sec^3(x)	\int\:_{0}^{\frac{π}{4}}6\sec^{3}(x)dx
limit as x approaches 2-of ((2)\|x\|)/x-x	\lim\:_{x\to\:2-}(\frac{(2)\left\|x\right\|}{x}-x)
integral of 4x-1	\int\:4x-1dx
integral from 0 to 5 of 6x-x^2	\int\:_{0}^{5}6x-x^{2}dx
derivative of ,x	\frac{d}{dx}(,x)
(dy)/(dx)= 1/(xy^3)	\frac{dy}{dx}=\frac{1}{xy^{3}}
area y=3x+2,y=x^3	area\:y=3x+2,y=x^{3}
inverse oflaplace 8/(s^2+8s)	inverselaplace\:\frac{8}{s^{2}+8s}
area y=0,y=x^3+8,[-3,-1]	area\:y=0,y=x^{3}+8,[-3,-1]
integral of 7sin^3(x)cos^5(x)	\int\:7\sin^{3}(x)\cos^{5}(x)dx
tangent of f(x)=sqrt(x+9),\at x=0	tangent\:f(x)=\sqrt{x+9},\at\:x=0
integral of (7x^2+3x-4)	\int\:(7x^{2}+3x-4)dx
limit as x approaches 2 of 3x^2+4x+10	\lim\:_{x\to\:2}(3x^{2}+4x+10)
integral from pi to 2pi of cos(x)	\int\:_{π}^{2π}\cos(x)dx
derivative of 4cot(x/7)	derivative\:4\cot(\frac{x}{7})
derivative of (8(2x^4+5)^3)	\frac{d}{dx}((8(2x)^{4}+5)^{3})
factor 2x^3-3x^2+5	factor\:2x^{3}-3x^{2}+5
x^'=2x	x^{\prime\:}=2x
(dy)/(dt)-y=2cos(kt),y(0)=7	\frac{dy}{dt}-y=2\cos(kt),y(0)=7
(dy)/(dt)=((4t+y))/(4y-t)	\frac{dy}{dt}=\frac{(4t+y)}{4y-t}
(dy)/(dx)=1+x^2+y^2+x^2y^2	\frac{dy}{dx}=1+x^{2}+y^{2}+x^{2}y^{2}
derivative of sqrt(x-2\sqrt{x-2)}	\frac{d}{dx}(\sqrt{x-2\sqrt{x-2}})
derivative of (1+x^{1/2})	\frac{d}{dx}((1+x)^{\frac{1}{2}})
integral of (cos(x))^2*sin(x)	\int\:(\cos(x))^{2}\cdot\:\sin(x)dx
derivative of x^2-x-ln(x)	\frac{d}{dx}(x^{2}-x-\ln(x))

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