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Popular Calculus Problems

d/(d{r)}({r}^3)	\frac{d}{d{r}}({r}^{3})
f(x)=arctan(4x)	f(x)=\arctan(4x)
integral of (5x^3-2x^2+3)	\int\:(5x^{3}-2x^{2}+3)dx
limit as x approaches 0 of (e^x-1)/(6x)	\lim\:_{x\to\:0}(\frac{e^{x}-1}{6x})
integral of x^4-4x^2+4	\int\:x^{4}-4x^{2}+4dx
integral of (4x+3)(2x^2+3x)^2	\int\:(4x+3)(2x^{2}+3x)^{2}dx
integral of (12x+24)/(x^2+4x+3)	\int\:\frac{12x+24}{x^{2}+4x+3}dx
derivative of sqrt(3x+2)	derivative\:\sqrt{3x+2}
(dy)/(dx)=e^{8x}+10y	\frac{dy}{dx}=e^{8x}+10y
derivative of ((3-5x^6)/(10))	\frac{d}{dx}(\frac{(3-5x)^{6}}{10})
integral of (32^x-23^x)/(2^x)	\int\:\frac{3\cdot\:2^{x}-2\cdot\:3^{x}}{2^{x}}dx
integral of x^22sin(x)	\int\:x^{2}2\sin(x)dx
derivative of (x^2)/(x+6)	derivative\:\frac{x^{2}}{x+6}
derivative of x^2e^x-e^x	\frac{d}{dx}(x^{2}e^{x}-e^{x})
limit as x approaches 6 of xpi+sqrt(x-3)	\lim\:_{x\to\:6}(xπ+\sqrt{x-3})
integral of 3x^2(x^3+4)^{10}	\int\:3x^{2}(x^{3}+4)^{10}dx
derivative of (5x/(1-x))	\frac{d}{dx}(\frac{5x}{1-x})
derivative of 2xsin(2x)	\frac{d}{dx}(2x\sin(2x))
y^{''}+2y^'+10y=cos(t)+0.739	y^{\prime\:\prime\:}+2y^{\prime\:}+10y=\cos(t)+0.739
derivative of f(x)=11x^3tan(x)	derivative\:f(x)=11x^{3}\tan(x)
derivative of (6x^2-12x+12e^x)	\frac{d}{dx}((6x^{2}-12x+12)e^{x})
integral of 1/(y^2-y)	\int\:\frac{1}{y^{2}-y}dy
slope of f(x)=x^2+2	slope\:f(x)=x^{2}+2
(\partial)/(\partial x)(xye^{x+y})	\frac{\partial\:}{\partial\:x}(xye^{x+y})
limit as x approaches 1 of (x^2+7x)/x	\lim\:_{x\to\:1}(\frac{x^{2}+7x}{x})
laplacetransform t^3	laplacetransform\:t^{3}
integral from-infinity to 0 of 1/(3-6x)	\int\:_{-\infty\:}^{0}\frac{1}{3-6x}dx
area y=e^x,y=e^{2x},x=ln(4)	area\:y=e^{x},y=e^{2x},x=\ln(4)
(cos(1/x))^'	(\cos(\frac{1}{x}))^{\prime\:}
integral of (30sqrt(x^2-49))/(x^4)	\int\:\frac{30\sqrt{x^{2}-49}}{x^{4}}dx
(\partial)/(\partial x)(x/(x-1))	\frac{\partial\:}{\partial\:x}(\frac{x}{x-1})
limit as x approaches 0 of 2x^2cos(5/x)	\lim\:_{x\to\:0}(2x^{2}\cos(\frac{5}{x}))
derivative of f(x)=5x^5ln(x)	derivative\:f(x)=5x^{5}\ln(x)
(dy)/(dx)= y/x+5x+4	\frac{dy}{dx}=\frac{y}{x}+5x+4
(\partial ^2)/(\partial y^2)(x^2-y^2)	\frac{\partial\:^{2}}{\partial\:y^{2}}(x^{2}-y^{2})
(\partial)/(\partial x)(14xe^y)	\frac{\partial\:}{\partial\:x}(14xe^{y})
x^2y^'=y^2+x^2	x^{2}y^{\prime\:}=y^{2}+x^{2}
derivative of (x+2e^{-x})	\frac{d}{dx}((x+2)e^{-x})
(dy)/(dx)= x/(34+x^2)	\frac{dy}{dx}=\frac{x}{34+x^{2}}
(dy)/(dx)=sqrt(9y)e^{x+3}	\frac{dy}{dx}=\sqrt{9y}e^{x+3}
integral of (3+16x)/(8x-4)	\int\:\frac{3+16x}{8x-4}dx
derivative of-x/4+3/4	\frac{d}{dx}(-\frac{x}{4}+\frac{3}{4})
integral of x^2e^{-2x}	\int\:x^{2}e^{-2x}dx
(-1/(4x^{3/2)})^'	(-\frac{1}{4x^{\frac{3}{2}}})^{\prime\:}
(dy)/(dx)+y^9x+9y=0	\frac{dy}{dx}+y^{9}x+9y=0
limit as x approaches 4 of x^2-2x-8	\lim\:_{x\to\:4}(x^{2}-2x-8)
derivative of (6x^2-6x+3(1+2x))	\frac{d}{dx}((6x^{2}-6x+3)(1+2x))
slope of (2.2)(4.3)	slope\:(2.2)(4.3)
limit as x approaches-2 of (x+3)/(x^2-2)	\lim\:_{x\to\:-2}(\frac{x+3}{x^{2}-2})
integral of-7e^x	\int\:-7e^{x}dx
limit as x approaches 2 of 0	\lim\:_{x\to\:2}(0)
integral of (tan(x)-(sin(x))/(cos(x)))	\int\:(\tan(x)-\frac{\sin(x)}{\cos(x)})dx
derivative of 2arcsin(x)	derivative\:2\arcsin(x)
limit as x approaches 9 of f(x)	\lim\:_{x\to\:9}(f(x))
integral of x^5sqrt(x^6+4)	\int\:x^{5}\sqrt{x^{6}+4}dx
derivative of 8/(2x+3)	\frac{d}{dx}(\frac{8}{2x+3})
integral of (x^{1/3}-3^{1/3})	\int\:(x^{\frac{1}{3}}-3^{\frac{1}{3}})dx
derivative of x^9ln(7x)	\frac{d}{dx}(x^{9}\ln(7x))
sum from n=1 to infinity of 1/(4n^2+5)	\sum\:_{n=1}^{\infty\:}\frac{1}{4n^{2}+5}
derivative of (5-sec(x)/(tan(x)))	\frac{d}{dx}(\frac{5-\sec(x)}{\tan(x)})
derivative of y=9	derivative\:y=9
tangent of f(x)=(sqrt(x)+1)/(sqrt(x)+3)	tangent\:f(x)=\frac{\sqrt{x}+1}{\sqrt{x}+3}
limit as x approaches 0-of 1/(x^3-2x^2)	\lim\:_{x\to\:0-}(\frac{1}{x^{3}-2x^{2}})
integral of (2x^2+x+19)/((x+1)(x^2+9))	\int\:\frac{2x^{2}+x+19}{(x+1)(x^{2}+9)}dx
tangent of f(x)=3x^2	tangent\:f(x)=3x^{2}
y^{''}-2y^'+y=(e^x)/(1+x^2)	y^{\prime\:\prime\:}-2y^{\prime\:}+y=\frac{e^{x}}{1+x^{2}}
integral from 0 to 2 of sqrt(x+2)	\int\:_{0}^{2}\sqrt{x+2}dx
integral of (2x+3)sin(x^2+3x+1)	\int\:(2x+3)\sin(x^{2}+3x+1)dx
(\partial)/(\partial z)(xe^{6y}sin(5z))	\frac{\partial\:}{\partial\:z}(xe^{6y}\sin(5z))
integral of e^{x^{1/2}}	\int\:e^{x^{\frac{1}{2}}}dx
derivative of y=(4x+3)^5	derivative\:y=(4x+3)^{5}
derivative of x^{-1/3}	derivative\:x^{-\frac{1}{3}}
derivative of f(x)=sqrt(x)-(x+6)^6	derivative\:f(x)=\sqrt{x}-(x+6)^{6}
limit as x approaches-2 of \sqrt[3]{x+1}	\lim\:_{x\to\:-2}(\sqrt[3]{x+1})
limit as x approaches 0 of (ln(1+10x))/x	\lim\:_{x\to\:0}(\frac{\ln(1+10x)}{x})
integral of sin(8x)sin(5x)	\int\:\sin(8x)\sin(5x)dx
integral of (sqrt(196-x^2))/x	\int\:\frac{\sqrt{196-x^{2}}}{x}dx
derivative of (1+9/x)^x	derivative\:(1+\frac{9}{x})^{x}
integral of (4x^3+3x^2+2x+5)	\int\:(4x^{3}+3x^{2}+2x+5)dx
limit as x approaches 3 of ((x^3f(x)-54))/(g(x)-1)	\lim\:_{x\to\:3}(\frac{(x^{3}f(x)-54)}{g(x)-1})
(\partial)/(\partial x)(ln(x)y)	\frac{\partial\:}{\partial\:x}(\ln(x)y)
derivative of sqrt(5+4{f)(x})	\frac{d}{dx}(\sqrt{5+4{f}(x)})
integral of 5x^4sin^2(x^5)	\int\:5x^{4}\sin^{2}(x^{5})dx
(dy)/(dx)=e^{2x-5y}	\frac{dy}{dx}=e^{2x-5y}
y^'=(x^2+2y^2)/(xy)	y^{\prime\:}=\frac{x^{2}+2y^{2}}{xy}
y^{''}-y^'-30=0	y^{\prime\:\prime\:}-y^{\prime\:}-30=0
derivative of 569+t(37t^{0.6}-108)	derivative\:569+t(37t^{0.6}-108)
(dr)/(dθ)=(r^2+10rθ)/(5θ^2)	\frac{dr}{dθ}=\frac{r^{2}+10rθ}{5θ^{2}}
integral of 5e^{2x-1}	\int\:5e^{2x-1}dx
y^{''}-18y^'+77y=0	y^{\prime\:\prime\:}-18y^{\prime\:}+77y=0
integral of x^{-2}ln(x)	\int\:x^{-2}\ln(x)dx
integral of x^5sin(x^2)	\int\:x^{5}\sin(x^{2})dx
tangent of y=(x+1)/(5-x),(7,-4)	tangent\:y=\frac{x+1}{5-x},(7,-4)
derivative of x^2cos(1/(x^2))	\frac{d}{dx}(x^{2}\cos(\frac{1}{x^{2}}))
limit as x approaches-2 of (x+1)/(x+2)	\lim\:_{x\to\:-2}(\frac{x+1}{x+2})
area y=sqrt(x),y=0,x=25	area\:y=\sqrt{x},y=0,x=25
y^'+2y=3x	y^{\prime\:}+2y=3x
derivative of sqrt(7x+4)	derivative\:\sqrt{7x+4}
integral from 1 to 2 of (x-1)^2	\int\:_{1}^{2}(x-1)^{2}dx
derivative of ln(x+b)	\frac{d}{dx}(\ln(x+b))

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