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Popular Calculus Problems

limit as x approaches infinity of-10e^{-2x}	\lim\:_{x\to\:\infty\:}(-10e^{-2x})
(dy)/(dt)= y/2	\frac{dy}{dt}=\frac{y}{2}
integral of 3x(x^2-4)^{1/2}	\int\:3x(x^{2}-4)^{\frac{1}{2}}dx
derivative of 3000(1+(4x/(x^2+100)))	\frac{d}{dx}(3000(1+\frac{4x}{x^{2}+100}))
(d^2)/(dx^2)(1)	\frac{d^{2}}{dx^{2}}(1)
2y^{''}+3y^'+4y=0	2y^{\prime\:\prime\:}+3y^{\prime\:}+4y=0
integral of sqrt(x)-x^4	\int\:\sqrt{x}-x^{4}dx
derivative of (5x-2/(2x+7))	\frac{d}{dx}(\frac{5x-2}{2x+7})
y^{''}-3y^'-28y=0	y^{\prime\:\prime\:}-3y^{\prime\:}-28y=0
limit as x approaches 0 of (e^{x^6}-1)/x	\lim\:_{x\to\:0}(\frac{e^{x^{6}}-1}{x})
integral of 4e^{-2x}	\int\:4e^{-2x}dx
integral of sqrt(3+x)	\int\:\sqrt{3+x}dx
integral of 2/(4x^2-1)	\int\:\frac{2}{4x^{2}-1}dx
derivative of (x^3+5)e^x	derivative\:(x^{3}+5)e^{x}
derivative of iny(x)	\frac{d}{dx}(iny(x))
integral from 1 to 10 of 1/(x^2-4x-32)	\int\:_{1}^{10}\frac{1}{x^{2}-4x-32}dx
derivative of g(x)= 1/(5x^2+4x)	derivative\:g(x)=\frac{1}{5x^{2}+4x}
integral from 3 to infinity of e^{-x/2}	\int\:_{3}^{\infty\:}e^{-\frac{x}{2}}dx
derivative of (arctan(4x)^2)	\frac{d}{dx}((\arctan(4x))^{2})
derivative of f(x)=4-x,x=-2,x=3,y=0	derivative\:f(x)=4-x,x=-2,x=3,y=0
laplacetransform t^3e^{-2t}-3cos(5t)	laplacetransform\:t^{3}e^{-2t}-3\cos(5t)
integral of x^2-8	\int\:x^{2}-8dx
integral of (5x^2-12x)e^{2x}	\int\:(5x^{2}-12x)e^{2x}dx
derivative of x/(sqrt(x^2+3))	\frac{d}{dx}(\frac{x}{\sqrt{x^{2}+3}})
derivative of (cot(x)/(sin(x)))	\frac{d}{dx}(\frac{\cot(x)}{\sin(x)})
derivative of x^3+x^2-x	\frac{d}{dx}(x^{3}+x^{2}-x)
limit as x approaches-2 of (-9)/(x^2)	\lim\:_{x\to\:-2}(\frac{-9}{x^{2}})
limit as x approaches infinity of (5)\sqrt[6666]{6}	\lim\:_{x\to\:\infty\:}((5)\sqrt[6666]{6})
y^{''}+6y^'+25y=100,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+6y^{\prime\:}+25y=100,y(0)=0,y^{\prime\:}(0)=0
(\partial)/(\partial x)(-e^xln(y))	\frac{\partial\:}{\partial\:x}(-e^{x}\ln(y))
inverse oflaplace e^{2s}	inverselaplace\:e^{2s}
limit as x approaches 4-of (7x-1)/(x-4)	\lim\:_{x\to\:4-}(\frac{7x-1}{x-4})
integral of (x^2+12x-9)/(x^3-9x)	\int\:\frac{x^{2}+12x-9}{x^{3}-9x}dx
y^{''}+13y^'+36y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+13y^{\prime\:}+36y=0,y(0)=1,y^{\prime\:}(0)=0
integral of-6sin^2(t)	\int\:-6\sin^{2}(t)dt
derivative of x^2(x-1)	\frac{d}{dx}(x^{2}(x-1))
integral of 1-t^{-0.52}	\int\:1-t^{-0.52}dt
tangent of sqrt(x-3)	tangent\:\sqrt{x-3}
integral of x^{22}e^{x^{23}}	\int\:x^{22}e^{x^{23}}dx
derivative of y=(3-x^2)(x^3-2x+1)	derivative\:y=(3-x^{2})(x^{3}-2x+1)
(dx}{dt}=\frac{1-x)/k	\frac{dx}{dt}=\frac{1-x}{k}
derivative of f(x)=sin(7ln(x))	derivative\:f(x)=\sin(7\ln(x))
xy^'=y+x^2sin(x),y(pi/2)=0	xy^{\prime\:}=y+x^{2}\sin(x),y(\frac{π}{2})=0
sum from n=0 to infinity of (x+3)^n	\sum\:_{n=0}^{\infty\:}(x+3)^{n}
integral from 0 to pi/2 of 6sin^2(3x)	\int\:_{0}^{\frac{π}{2}}6\sin^{2}(3x)dx
x*(dy)/(dx)-y=sqrt(x^2+y^2)	x\cdot\:\frac{dy}{dx}-y=\sqrt{x^{2}+y^{2}}
derivative of 64sin(4x)	\frac{d}{dx}(64\sin(4x))
d/(dt)((2t)/(2t^2+1))	\frac{d}{dt}(\frac{2t}{2t^{2}+1})
integral of-3sec(x)tan(x)-3csc(x)cot(x)	\int\:-3\sec(x)\tan(x)-3\csc(x)\cot(x)dx
integral of 1/(6x)	\int\:\frac{1}{6x}dx
(t-sin(t))^'	(t-\sin(t))^{\prime\:}
sum from n=1 to infinity of 4/(nln(8n))	\sum\:_{n=1}^{\infty\:}\frac{4}{n\ln(8n)}
derivative of f(x)=sqrt(17x)	derivative\:f(x)=\sqrt{17x}
derivative of (8t)/(8+sqrt(t))	derivative\:\frac{8t}{8+\sqrt{t}}
integral of (3x^2)/2	\int\:\frac{3x^{2}}{2}dx
(\partial)/(\partial x)(3x^{1/3}y^{2/3})	\frac{\partial\:}{\partial\:x}(3x^{\frac{1}{3}}y^{\frac{2}{3}})
integral of 1/(7xlog_{3)(x)}	\int\:\frac{1}{7x\log_{3}(x)}dx
(\partial)/(\partial x)(ycos(xlog_{e}(y)))	\frac{\partial\:}{\partial\:x}(y\cos(x\log_{e}(y)))
(dy)/(dt)=-3(y-5)	\frac{dy}{dt}=-3(y-5)
limit as x approaches infinity of ((\frac{x+1)/(x^3+2))}{(x/(x^3))}	\lim\:_{x\to\:\infty\:}(\frac{(\frac{x+1}{x^{3}+2})}{(\frac{x}{x^{3}})})
limit as x approaches 5+of 8/(x-5)	\lim\:_{x\to\:5+}(\frac{8}{x-5})
derivative of 2sin(2x-2cos(2x)-1/5 e^x)	\frac{d}{dx}(2\sin(2x)-2\cos(2x)-\frac{1}{5}e^{x})
y=-80+208	y=-80+208
(\partial)/(\partial y)(tan(x)y^{2.5})	\frac{\partial\:}{\partial\:y}(\tan(x)y^{2.5})
derivative of f(x)=-1/3 t^3+64t+3000	derivative\:f(x)=-\frac{1}{3}t^{3}+64t+3000
integral of ((x-7))/(x^2-18x+82)	\int\:\frac{(x-7)}{x^{2}-18x+82}dx
integral of sin(3x)tan(3x)	\int\:\sin(3x)\tan(3x)dx
sum from n=2 to infinity of ne^{-2n}	\sum\:_{n=2}^{\infty\:}ne^{-2n}
derivative of 2x^2cos(2x)	\frac{d}{dx}(2x^{2}\cos(2x))
tangent of y^2+5x=x^2y-5,(3,5)	tangent\:y^{2}+5x=x^{2}y-5,(3,5)
area x=y^2,x=3-2y^2	area\:x=y^{2},x=3-2y^{2}
integral of (3x)/(sqrt(x^4+6x^2+5))	\int\:\frac{3x}{\sqrt{x^{4}+6x^{2}+5}}dx
derivative of (x^3-1/2)	\frac{d}{dx}(\frac{x^{3}-1}{2})
(\partial)/(\partial x)(2xcos(x))	\frac{\partial\:}{\partial\:x}(2x\cos(x))
(d^4)/(dx^4)(x^x)	\frac{d^{4}}{dx^{4}}(x^{x})
integral of e^{1/y}	\int\:e^{\frac{1}{y}}dy
derivative of 4sqrt(x)-2x	derivative\:4\sqrt{x}-2x
derivative of log_{2}(e^{-x}cos(pix))	derivative\:\log_{2}(e^{-x}\cos(πx))
implicit (dy)/(dx),x^3-3x^2y+2xy^2=12	implicit\:\frac{dy}{dx},x^{3}-3x^{2}y+2xy^{2}=12
derivative of x^2(1-6x)	derivative\:x^{2}(1-6x)
derivative of x^5e^{-3ln(x})	\frac{d}{dx}(x^{5}e^{-3\ln(x)})
integral of sec^2(5xta)n^35x	\int\:\sec^{2}(5xta)n^{3}5xdx
integral of cos(x)cos(5x)	\int\:\cos(x)\cos(5x)dx
area f(x)=x^2,(1,5),5	area\:f(x)=x^{2},(1,5),5
derivative of arccsc(2x^4-5)	derivative\:\arccsc(2x^{4}-5)
integral of sin(4x)\sqrt[3]{cos(4x)}	\int\:\sin(4x)\sqrt[3]{\cos(4x)}dx
integral of pi/4	\int\:\frac{π}{4}
derivative of 3x^2+4x+5	\frac{d}{dx}(3x^{2}+4x+5)
laplacetransform 3(t-pi)	laplacetransform\:3(t-π)
limit as x approaches infinity of (1-5x)^{5/x}	\lim\:_{x\to\:\infty\:}((1-5x)^{\frac{5}{x}})
derivative of 7y	derivative\:7y
integral of 1/(16x^4+8x^2+1)	\int\:\frac{1}{16x^{4}+8x^{2}+1}dx
(\partial)/(\partial x)(sin(kx))	\frac{\partial\:}{\partial\:x}(\sin(kx))
tangent of y=7e^{-6x},(0,7)	tangent\:y=7e^{-6x},(0,7)
(dy)/(dx)=9x-y/x	\frac{dy}{dx}=9x-\frac{y}{x}
derivative of (6x-x^2^{1/2})	\frac{d}{dx}((6x-x^{2})^{\frac{1}{2}})
integral of tcos(t)sin(t)	\int\:t\cos(t)\sin(t)dt
integral of sqrt((9-x)/(9+x))	\int\:\sqrt{\frac{9-x}{9+x}}dx
derivative of f(x)=(e^2)/(x^2-2x)	derivative\:f(x)=\frac{e^{2}}{x^{2}-2x}
integral of (7/(sqrt(x)))	\int\:(\frac{7}{\sqrt{x}})dx

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