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Popular Calculus Problems

derivative of e^{2x^{2x}}	derivative\:e^{2x^{2x}}
limit as x approaches 1 of (x-1)^{-1}	\lim\:_{x\to\:1}((x-1)^{-1})
tangent of f(x)=cos^3(x),\at (0)	tangent\:f(x)=\cos^{3}(x),\at\:(0)
(\partial)/(\partial x)((x-2y)/(x+2))	\frac{\partial\:}{\partial\:x}(\frac{x-2y}{x+2})
sum from n=1 to infinity of (4n)/(7n+1)	\sum\:_{n=1}^{\infty\:}\frac{4n}{7n+1}
sum from n=1 to infinity of 2^{n-1}	\sum\:_{n=1}^{\infty\:}2^{n-1}
integral from 0 to pi/6 of (1-cos(3x))sin(3x)	\int\:_{0}^{\frac{π}{6}}(1-\cos(3x))\sin(3x)dx
derivative of 4e^{2x}	derivative\:4e^{2x}
derivative of 3x^2+1	\frac{d}{dx}(3x^{2}+1)
sum from n=0 to infinity of 1/4	\sum\:_{n=0}^{\infty\:}\frac{1}{4}
integral from 7 to 12 of y/(y^2-3y-4)	\int\:_{7}^{12}\frac{y}{y^{2}-3y-4}dy
integral of xsin(2x)	\int\:x\sin(2x)dx
derivative of x/y+e^y	\frac{d}{dx}(\frac{x}{y}+e^{y})
integral of 5^x-sec^2(x)	\int\:5^{x}-\sec^{2}(x)dx
integral of (\sqrt[3]{u}+1/(sqrt(u)))	\int\:(\sqrt[3]{u}+\frac{1}{\sqrt{u}})du
area-x^2-1,x^2+4,[-2,3]	area\:-x^{2}-1,x^{2}+4,[-2,3]
y^'=x(1+y)	y^{\prime\:}=x(1+y)
(\partial)/(\partial x)(tsqrt(x))	\frac{\partial\:}{\partial\:x}(t\sqrt{x})
integral of-1/2 x	\int\:-\frac{1}{2}xdx
integral of (x^3)/6	\int\:\frac{x^{3}}{6}dx
derivative of y=(9000)/(x^2)	derivative\:y=\frac{9000}{x^{2}}
(\partial)/(\partial x)(4xyz+ln(2xyz))	\frac{\partial\:}{\partial\:x}(4xyz+\ln(2xyz))
(sqrt(2x^4+1))/y y^'+1/6 y^3x^3=0	\frac{\sqrt{2x^{4}+1}}{y}y^{\prime\:}+\frac{1}{6}y^{3}x^{3}=0
y^'-y^2=36	y^{\prime\:}-y^{2}=36
integral from 0 to 1 of (30)/(4y-1)	\int\:_{0}^{1}\frac{30}{4y-1}dy
x*(dy)/(dx)=4y	x\cdot\:\frac{dy}{dx}=4y
factor f(e^{2x})	factor\:f(e^{2x})
(\partial)/(\partial y)(arcsin(x-y))	\frac{\partial\:}{\partial\:y}(\arcsin(x-y))
integral of x^{1/2}sin(x^{3/2}+1)	\int\:x^{\frac{1}{2}}\sin(x^{\frac{3}{2}}+1)dx
integral of (5u-1)(3u^3+2)	\int\:(5u-1)(3u^{3}+2)du
integral of 1/(x(ln(x))^{10)}	\int\:\frac{1}{x(\ln(x))^{10}}dx
derivative of (tan^3(x)/(2x+1))	\frac{d}{dx}(\frac{\tan^{3}(x)}{2x+1})
integral of sin(4-x)	\int\:\sin(4-x)dx
limit as x approaches 0 of ln\|sin(x)\|	\lim\:_{x\to\:0}(\ln\left\|\sin(x)\right\|)
derivative of (4x^3/3-x+2e^x)	\frac{d}{dx}(\frac{4x^{3}}{3}-x+2e^{x})
18y^{''}-9y^'-5y=0	18y^{\prime\:\prime\:}-9y^{\prime\:}-5y=0
(dy)/(dx)+4xy=0	\frac{dy}{dx}+4xy=0
slope of (10,-3),(7,1)	slope\:(10,-3),(7,1)
limit as x approaches 0 of x^{sin(x)}	\lim\:_{x\to\:0}(x^{\sin(x)})
(x^2-1)y^'+2y=(x+1)^2	(x^{2}-1)y^{\prime\:}+2y=(x+1)^{2}
d/(dp)(e^p(p+psqrt(p)))	\frac{d}{dp}(e^{p}(p+p\sqrt{p}))
limit as x approaches-4 of x^2	\lim\:_{x\to\:-4}(x^{2})
laplacetransform 5	laplacetransform\:5
integral of 5/t	\int\:\frac{5}{t}dt
integral of 1/(3(x^2+1))	\int\:\frac{1}{3(x^{2}+1)}dx
tangent of y=(3x)/(2^x),\at x=2	tangent\:y=\frac{3x}{2^{x}},\at\:x=2
integral of (e^x+1)/(e^{2x)-1}	\int\:\frac{e^{x}+1}{e^{2x}-1}dx
((x^2-2)/(5x^3+6))^'	(\frac{x^{2}-2}{5x^{3}+6})^{\prime\:}
y^{''}-2y^'+y=0,y(0)=5,y^'(0)=10	y^{\prime\:\prime\:}-2y^{\prime\:}+y=0,y(0)=5,y^{\prime\:}(0)=10
(\partial)/(\partial x)(tanh(x))	\frac{\partial\:}{\partial\:x}(\tanh(x))
limit as x approaches 0 of (tan(5x))/x	\lim\:_{x\to\:0}(\frac{\tan(5x)}{x})
integral of 1/(x^3)-x	\int\:\frac{1}{x^{3}}-xdx
derivative of x^3(x-3^2)	\frac{d}{dx}(x^{3}(x-3)^{2})
limit as x approaches 0 of 2	\lim\:_{x\to\:0}(2)
derivative of 1/3 x^3+2x-4	\frac{d}{dx}(\frac{1}{3}x^{3}+2x-4)
sum from n=0 to infinity of (6/5)^n	\sum\:_{n=0}^{\infty\:}(\frac{6}{5})^{n}
tangent of f(x)=x^3-x	tangent\:f(x)=x^{3}-x
integral of 4t^3cos(t^4+1)	\int\:4t^{3}\cos(t^{4}+1)dt
derivative of 1/(arctan(x))	derivative\:\frac{1}{\arctan(x)}
integral of (x^2+5)^3x	\int\:(x^{2}+5)^{3}xdx
derivative of 5-2x	derivative\:5-2x
integral of x(x^2-1)^{99}	\int\:x(x^{2}-1)^{99}dx
sum from n=0 to infinity of 1/(n+9)	\sum\:_{n=0}^{\infty\:}\frac{1}{n+9}
integral of x^3+3	\int\:x^{3}+3dx
(dy)/(dx)=2x-y,y(0)=1	\frac{dy}{dx}=2x-y,y(0)=1
limit as x approaches 2 of x^2+3x+5	\lim\:_{x\to\:2}(x^{2}+3x+5)
(\partial)/(\partial x)(e^{-x^2-y^2})	\frac{\partial\:}{\partial\:x}(e^{-x^{2}-y^{2}})
integral of sqrt(1+cos(4x))	\int\:\sqrt{1+\cos(4x)}dx
derivative of 5sin(x-sin(5x))	\frac{d}{dx}(5\sin(x)-\sin(5x))
inverse oflaplace (e^{-6s})/(s^2+2s-8)	inverselaplace\:\frac{e^{-6s}}{s^{2}+2s-8}
integral of (4x+x^2)/(x^2)	\int\:\frac{4x+x^{2}}{x^{2}}dx
(\partial)/(\partial x)(xyz-z-sin(x+y))	\frac{\partial\:}{\partial\:x}(xyz-z-\sin(x+y))
derivative of f(x)=ln((x-2)/(x+1))	derivative\:f(x)=\ln(\frac{x-2}{x+1})
integral of x(7-y)	\int\:x(7-y)
integral of 1/(9-4x^2)	\int\:\frac{1}{9-4x^{2}}dx
integral from 0 to infinity of f(a+x)	\int\:_{0}^{\infty\:}f(a+x)dx
sum from n=0 to infinity of 3/((1+i)^n)	\sum\:_{n=0}^{\infty\:}\frac{3}{(1+i)^{n}}
implicit (dy)/(dx),e^y=x	implicit\:\frac{dy}{dx},e^{y}=x
d/(du)(usin(v))	\frac{d}{du}(u\sin(v))
derivative of 3+x^2	\frac{d}{dx}(3+x^{2})
y^{''}+5y=-180x^2e^5x	y^{\prime\:\prime\:}+5y=-180x^{2}e^{5}x
f(x)=x-ln(x)	f(x)=x-\ln(x)
slope of (-4,-3),(8,-9)	slope\:(-4,-3),(8,-9)
integral of x^3in(3x)	\int\:x^{3}in(3x)dx
d/(dy)(cos(x^2y))	\frac{d}{dy}(\cos(x^{2}y))
sum from n=2 to infinity of (ln^2(n))/n	\sum\:_{n=2}^{\infty\:}\frac{\ln^{2}(n)}{n}
integral from 0 to x of sqrt(2/(1+t))	\int\:_{0}^{x}\sqrt{\frac{2}{1+t}}dt
derivative of cos^3(5x+1)	\frac{d}{dx}(\cos^{3}(5x+1))
y^{''}+4y=-6,y(pi/8)=-12,y^'(pi/8)=2	y^{\prime\:\prime\:}+4y=-6,y(\frac{π}{8})=-12,y^{\prime\:}(\frac{π}{8})=2
derivative of (x-1e^{-x})	\frac{d}{dx}((x-1)e^{-x})
derivative of e^{3xy}	\frac{d}{dx}(e^{3xy})
limit as h approaches 0 of ((f(h)(4+h)-f(4)))/h	\lim\:_{h\to\:0}(\frac{(f(h)(4+h)-f(4))}{h})
(\partial)/(\partial x)(e^{-x}cos(y))	\frac{\partial\:}{\partial\:x}(e^{-x}\cos(y))
slope of y=x^3	slope\:y=x^{3}
xy^'+xy=1-y	xy^{\prime\:}+xy=1-y
(2xy^2-3y^3)dx+(7-3xy^2)dy=0	(2xy^{2}-3y^{3})dx+(7-3xy^{2})dy=0
f(x)=x*e^{1/x}	f(x)=x\cdot\:e^{\frac{1}{x}}
integral of sec^3(3x)tan(3x)	\int\:\sec^{3}(3x)\tan(3x)dx
derivative of 9/(2x^2)	\frac{d}{dx}(\frac{9}{2x^{2}})
(dy)/(dx)=20-y	\frac{dy}{dx}=20-y

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