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Popular Calculus Problems

limit as x approaches 0 of (x)^x	\lim\:_{x\to\:0}((x)^{x})
y^'=(5x)/y	y^{\prime\:}=\frac{5x}{y}
(\partial)/(\partial x)(e^{x*y})	\frac{\partial\:}{\partial\:x}(e^{x\cdot\:y})
derivative of e^{-x}sin(pix)	\frac{d}{dx}(e^{-x}\sin(π)x)
derivative of (8x)^{6x}	derivative\:(8x)^{6x}
derivative of 6xe^{-x^2}	derivative\:6xe^{-x^{2}}
limit as x approaches infinity of-e^{2x}	\lim\:_{x\to\:\infty\:}(-e^{2x})
y^'=x+y,y(0)=3	y^{\prime\:}=x+y,y(0)=3
(dy)/(dx)+5y=70	\frac{dy}{dx}+5y=70
integral of (1+tan(x))	\int\:(1+\tan(x))dx
integral of xtan^4(x^2)	\int\:x\tan^{4}(x^{2})dx
integral of 6/(x^4)	\int\:\frac{6}{x^{4}}dx
limit as x approaches-2-of (-6x)/(x+2)	\lim\:_{x\to\:-2-}(\frac{-6x}{x+2})
integral from 0 to 7 of 1/(sqrt(49-t^2))	\int\:_{0}^{7}\frac{1}{\sqrt{49-t^{2}}}dt
integral from 0 to 2 of (2x)/((1+x^2)^2)	\int\:_{0}^{2}\frac{2x}{(1+x^{2})^{2}}dx
integral of 3x^34x^4	\int\:3x^{3}4x^{4}dx
limit as x approaches 1 of 2x^3-4x^2+x+8	\lim\:_{x\to\:1}(2x^{3}-4x^{2}+x+8)
derivative of 9x+4	derivative\:9x+4
y^{''}+2y^'+5y=5sin(2t)	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=5\sin(2t)
derivative of y=(e^x+4)^3	derivative\:y=(e^{x}+4)^{3}
y^{''}-3y^'+2y=e^x+2e^{3x}	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=e^{x}+2e^{3x}
d/(d{z)}({y}{z})	\frac{d}{d{z}}({y}{z})
(\partial)/(\partial x)(2xy-x^2+y)	\frac{\partial\:}{\partial\:x}(2xy-x^{2}+y)
integral from 0 to 1 of pi(4-3/2 x)^2	\int\:_{0}^{1}π(4-\frac{3}{2}x)^{2}dx
limit as x approaches infinity of (10x+100)/(x^2-30)	\lim\:_{x\to\:\infty\:}(\frac{10x+100}{x^{2}-30})
y(t+2)y^'+1=-t	y(t+2)y^{\prime\:}+1=-t
integral from 0 to 2 of 2pi(3-x)(8-x^3)	\int\:_{0}^{2}2π(3-x)(8-x^{3})dx
derivative of (x^2(4x+1))	\frac{d}{dx}((x)^{2}(4x+1))
integral of (sqrt(y^2-36))/y	\int\:\frac{\sqrt{y^{2}-36}}{y}dy
integral of ((2+3sin^2(x))/(sin^2(x)))	\int\:(\frac{2+3\sin^{2}(x)}{\sin^{2}(x)})dx
derivative of 1/(x^2+1/x+x)	\frac{d}{dx}(\frac{1}{x^{2}}+\frac{1}{x}+x)
integral of x 1/(x^2)	\int\:x\frac{1}{x^{2}}dx
derivative of (4sqrt(x)/(x^2-2))	\frac{d}{dx}(\frac{4\sqrt{x}}{x^{2}-2})
integral of 1/((x+3)(x-2)^2)	\int\:\frac{1}{(x+3)(x-2)^{2}}dx
integral of (3e^x+2sin(x))	\int\:(3e^{x}+2\sin(x))dx
derivative of f(x)=3x^2+2x-4	derivative\:f(x)=3x^{2}+2x-4
tangent of y=(1+5x)^9,(0,1)	tangent\:y=(1+5x)^{9},(0,1)
integral of 1/((x+4)^2)	\int\:\frac{1}{(x+4)^{2}}dx
limit as x approaches 8 of x/(x-8)	\lim\:_{x\to\:8}(\frac{x}{x-8})
(dy)/(dx)y=(x^2+1)^3	\frac{dy}{dx}y=(x^{2}+1)^{3}
slope of y=3+5x^2-2x^3	slope\:y=3+5x^{2}-2x^{3}
(\partial)/(\partial x)((x-2)^2+(5-x-y)^2)	\frac{\partial\:}{\partial\:x}((x-2)^{2}+(5-x-y)^{2})
limit as x approaches 7 of-x^2+3x-8	\lim\:_{x\to\:7}(-x^{2}+3x-8)
(\partial)/(\partial x)(8x^6y^4+9x^5y^7)	\frac{\partial\:}{\partial\:x}(8x^{6}y^{4}+9x^{5}y^{7})
(\partial)/(\partial x)((-x)/((x+y)^2))	\frac{\partial\:}{\partial\:x}(\frac{-x}{(x+y)^{2}})
f(x)=sech(x)	f(x)=\sech(x)
derivative of ((x^2+5)/(x^2-5))^2	derivative\:(\frac{x^{2}+5}{x^{2}-5})^{2}
integral of sin(0)	\int\:\sin(0)
integral of (6x^2-8x+3)	\int\:(6x^{2}-8x+3)dx
derivative of 2xtan(x+x^2sec^2(x))	\frac{d}{dx}(2x\tan(x)+x^{2}\sec^{2}(x))
derivative of cos(pix^2)	\frac{d}{dx}(\cos(πx^{2}))
sum from n=1 to infinity of 1/(4n^2-1)	\sum\:_{n=1}^{\infty\:}\frac{1}{4n^{2}-1}
expand-2x^2(x+4)	expand\:-2x^{2}(x+4)
integral from-2 to 2 of (x^3-3x^2+2)	\int\:_{-2}^{2}(x^{3}-3x^{2}+2)dx
derivative of sinh^2(x/(1+x))	\frac{d}{dx}(\sinh^{2}(\frac{x}{1+x}))
integral of (50x+6)/((7x+1)(x-1))	\int\:\frac{50x+6}{(7x+1)(x-1)}dx
integral of e^{4x+6}	\int\:e^{4x+6}dx
y^'=(2y)/x-xy^2	y^{\prime\:}=\frac{2y}{x}-xy^{2}
area 6sin(θ),6cos(θ)	area\:6\sin(θ),6\cos(θ)
integral of (sqrt(ln(4x)))/x	\int\:\frac{\sqrt{\ln(4x)}}{x}dx
derivative of x/(x^2-5)	derivative\:\frac{x}{x^{2}-5}
derivative of ln(n)	derivative\:\ln(n)
(\partial)/(\partial x)(x^2-4xy)	\frac{\partial\:}{\partial\:x}(x^{2}-4xy)
integral of e^{7x}sin(8x)	\int\:e^{7x}\sin(8x)dx
y^'=x*y	y^{\prime\:}=x\cdot\:y
(\partial)/(\partial x)(x^7+4^y+x^y)	\frac{\partial\:}{\partial\:x}(x^{7}+4^{y}+x^{y})
taylor (e^{2x}),-2	taylor\:(e^{2x}),-2
derivative of (e^{-x}/(x+1))	\frac{d}{dx}(\frac{e^{-x}}{x+1})
derivative of (0.3(5^x)/(x^3))	\frac{d}{dx}(\frac{0.3(5^{x})}{x^{3}})
derivative of (2x-21(x^2+36))	\frac{d}{dx}((2x-21)(x^{2}+36))
derivative of x*(x^2+1^{1/2})	\frac{d}{dx}(x\cdot\:(x^{2}+1)^{\frac{1}{2}})
limit as x approaches infinity of (5x)/(7x-4x^3)	\lim\:_{x\to\:\infty\:}(\frac{5x}{7x-4x^{3}})
sum from n=1 to infinity of n/(n^2)	\sum\:_{n=1}^{\infty\:}\frac{n}{n^{2}}
derivative of y=tan^4(x)	derivative\:y=\tan^{4}(x)
derivative of f(x)=e^{x^6}	derivative\:f(x)=e^{x^{6}}
integral from 2 to infinity of 8/(x^2)	\int\:_{2}^{\infty\:}\frac{8}{x^{2}}dx
derivative of ((5x^3)/((1-5x)^4))	\frac{d}{dx}(\frac{(5x^{3})}{(1-5x)^{4}})
y^{''}-4y^'+4y=e^{-t}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=e^{-t}
integral of 16x(8x^2+2)^6	\int\:16x(8x^{2}+2)^{6}dx
(d^2y)/(dx^2)-y=2e^x+6e^{2x}	\frac{d^{2}y}{dx^{2}}-y=2e^{x}+6e^{2x}
(\partial)/(\partial x)(2xcos(x)cos(y))	\frac{\partial\:}{\partial\:x}(2x\cos(x)\cos(y))
integral from 0 to 4 of x+2	\int\:_{0}^{4}x+2dx
(d^2)/(dx^2)(e^{4x})	\frac{d^{2}}{dx^{2}}(e^{4x})
derivative of (3x^2-4xe^{5x})	\frac{d}{dx}((3x^{2}-4x)e^{5x})
(d^2)/(dx^2)(x^2e^{2x})	\frac{d^{2}}{dx^{2}}(x^{2}e^{2x})
area x=4-y^2,x=y-2	area\:x=4-y^{2},x=y-2
derivative of sin(3cos(x))	\frac{d}{dx}(\sin(3\cos(x)))
(\partial)/(\partial s)(st^2)	\frac{\partial\:}{\partial\:s}(st^{2})
y^'(x^2+1)+9x(y-1)=0	y^{\prime\:}(x^{2}+1)+9x(y-1)=0
limit as x approaches 0+of ax^x+1	\lim\:_{x\to\:0+}(ax^{x}+1)
(dy)/(dx)+4y=3	\frac{dy}{dx}+4y=3
y'+y=y^2	y\prime\:+y=y^{2}
integral of (5x^2+2)/(x^4)	\int\:\frac{5x^{2}+2}{x^{4}}dx
derivative of (\sqrt[3]{x}-2xe^x/x)	\frac{d}{dx}(\frac{\sqrt[3]{x}-2xe^{x}}{x})
integral from 1 to 2 of 2x^2sqrt(x^3+1)	\int\:_{1}^{2}2x^{2}\sqrt{x^{3}+1}dx
derivative of (e^x/(sin(2x)))	\frac{d}{dx}(\frac{e^{x}}{\sin(2x)})
integral of x(2x^2+3)^4	\int\:x(2x^{2}+3)^{4}dx
limit as x approaches 0 of (sin(x))/(-x)	\lim\:_{x\to\:0}(\frac{\sin(x)}{-x})
d/(d{y)}({x}^{({y})/({z)}})	\frac{d}{d{y}}({x}^{\frac{{y}}{{z}}})
derivative of-sin(x^2)	derivative\:-\sin(x^{2})

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