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Popular Calculus Problems

limit as x approaches 1 of x/(ln(1+x))	\lim\:_{x\to\:1}(\frac{x}{\ln(1+x)})
tangent of y=x+e^x-1/x ,\at x=1	tangent\:y=x+e^{x}-\frac{1}{x},\at\:x=1
derivative of (-3x^2-3)^4	derivative\:(-3x^{2}-3)^{4}
limit as x approaches 2 of x^2+sqrt(x+2)	\lim\:_{x\to\:2}(x^{2}+\sqrt{x+2})
(\partial)/(\partial x)(x^2yz^2+sin(yz))	\frac{\partial\:}{\partial\:x}(x^{2}yz^{2}+\sin(yz))
derivative of 2+sin(3x)	\frac{d}{dx}(2+\sin(3x))
integral of sin(x^2+y^2)	\int\:\sin(x^{2}+y^{2})
A^'	A^{\prime\:}
integral of 2sin(2x)cos(2x)	\int\:2\sin(2x)\cos(2x)dx
integral of ((x-1))/((x+4))	\int\:\frac{(x-1)}{(x+4)}dx
integral of 3/(x^4)	\int\:\frac{3}{x^{4}}dx
derivative of f(x)=-(x^3+x-1)/2	derivative\:f(x)=-\frac{x^{3}+x-1}{2}
derivative of sqrt(e^{2x)+2+e^{-2x}}	\frac{d}{dx}(\sqrt{e^{2x}+2+e^{-2x}})
derivative of 1/a e^{ax}	\frac{d}{dx}(\frac{1}{a}e^{ax})
integral from 0 to pi/2 of sin^2(x)	\int\:_{0}^{\frac{π}{2}}\sin^{2}(x)dx
integral from 1 to e^3 of x^3ln(x)	\int\:_{1}^{e^{3}}x^{3}\ln(x)dx
y^{''}-2y^'-3y=4x-5+6xe^{2x}	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=4x-5+6xe^{2x}
integral of 3cos(x)sin(x)	\int\:3\cos(x)\sin(x)dx
sum from n=1 to infinity of (n^2)/(2^n)	\sum\:_{n=1}^{\infty\:}\frac{n^{2}}{2^{n}}
derivative of (6x-1^2)	\frac{d}{dx}((6x-1)^{2})
(\partial)/(\partial x)((2xy)(sqrt(x^2+y^2)))	\frac{\partial\:}{\partial\:x}((2xy)(\sqrt{x^{2}+y^{2}}))
(\partial)/(\partial x)(sqrt(7-x^3-y^7))	\frac{\partial\:}{\partial\:x}(\sqrt{7-x^{3}-y^{7}})
integral of sec(x)(tan(x)-sec(x))	\int\:\sec(x)(\tan(x)-\sec(x))dx
integral of (e^x-1)/x	\int\:\frac{e^{x}-1}{x}dx
(\partial)/(\partial x)(7xy)	\frac{\partial\:}{\partial\:x}(7xy)
integral of (4x-csc^2(x))	\int\:(4x-\csc^{2}(x))dx
integral from 0 to pi/2 of sin(x)	\int\:_{0}^{\frac{π}{2}}\sin(x)dx
integral of 2tan^3(x)	\int\:2\tan^{3}(x)dx
integral of (e^{-x})/(1+e^{-x)}	\int\:\frac{e^{-x}}{1+e^{-x}}dx
derivative of 4(sin(x+xcos(x)))	\frac{d}{dx}(4(\sin(x)+x\cos(x)))
(dy)/(dx)=8xe^y	\frac{dy}{dx}=8xe^{y}
derivative of 3^{x+1}	\frac{d}{dx}(3^{x+1})
integral from 4 to 5 of (x^3-pix^2)	\int\:_{4}^{5}(x^{3}-πx^{2})dx
y^{''}+2y^'+2y=e^{-x}(8cos(x)-6sin(x))	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=e^{-x}(8\cos(x)-6\sin(x))
sum from n=0 to infinity of 2^{1/n}	\sum\:_{n=0}^{\infty\:}2^{\frac{1}{n}}
derivative of 4x^3-52x^2+160x	\frac{d}{dx}(4x^{3}-52x^{2}+160x)
d/(dz)(ln(z))	\frac{d}{dz}(\ln(z))
integral of 3x+7	\int\:3x+7dx
((x+1)dy)/(dx)=x	\frac{(x+1)dy}{dx}=x
derivative of x/(x-3-arcsec(2x))	\frac{d}{dx}(\frac{x}{x-3}-\arcsec(2x))
limit as x approaches 0 of x/(tan(x))	\lim\:_{x\to\:0}(\frac{x}{\tan(x)})
25y^{''}-40y^'+16y=0	25y^{\prime\:\prime\:}-40y^{\prime\:}+16y=0
integral of cos^2(x)sin^2(x)	\int\:\cos^{2}(x)\sin^{2}(x)dx
(2y^2+3xy)+(2xy+x^2)y^'=0	(2y^{2}+3xy)+(2xy+x^{2})y^{\prime\:}=0
x^{''}+9x=0,x(0)=0.7,x^'(0)=0.4	x^{\prime\:\prime\:}+9x=0,x(0)=0.7,x^{\prime\:}(0)=0.4
limit as x approaches 2 of-x^2	\lim\:_{x\to\:2}(-x^{2})
integral of 7xsqrt(1-x^4)	\int\:7x\sqrt{1-x^{4}}dx
derivative of 1/(2x-5)	\frac{d}{dx}(\frac{1}{2x-5})
derivative of f(2)=4log_{6}(x)	derivative\:f(2)=4\log_{6}(x)
derivative of 2^x+3	\frac{d}{dx}(2^{x}+3)
xy^'+y(1+ln(xy))=0	xy^{\prime\:}+y(1+\ln(xy))=0
integral of 8sqrt(x)	\int\:8\sqrt{x}dx
derivative of (3x^2+4x-2/x)	\frac{d}{dx}(\frac{3x^{2}+4x-2}{x})
derivative of 5/x	derivative\:\frac{5}{x}
integral of x/(a^2+x^2)	\int\:\frac{x}{a^{2}+x^{2}}dx
derivative of xy+8	\frac{d}{dx}(xy+8)
limit as h approaches 0 of 4h-h^2	\lim\:_{h\to\:0}(4h-h^{2})
integral of (9-162x)/(sqrt(25-81x^2))	\int\:\frac{9-162x}{\sqrt{25-81x^{2}}}dx
sum from n=0 to infinity of (n+1)!	\sum\:_{n=0}^{\infty\:}(n+1)!
limit as x approaches 0+of 3ln(x)+5/x	\lim\:_{x\to\:0+}(3\ln(x)+\frac{5}{x})
limit as x approaches 0 of-1/(4x)	\lim\:_{x\to\:0}(-\frac{1}{4x})
integral from 5 to 15 of (2x-1)	\int\:_{5}^{15}(2x-1)dx
(\partial)/(\partial x)(5x-8y^3)	\frac{\partial\:}{\partial\:x}(5x-8y^{3})
derivative of sqrt(5x+4)	derivative\:\sqrt{5x+4}
(d^2)/(dx^2)(sqrt(x^2+81))	\frac{d^{2}}{dx^{2}}(\sqrt{x^{2}+81})
derivative of x^3e^{sqrt(x)}	\frac{d}{dx}(x^{3}e^{\sqrt{x}})
integral of 1/(e^{kx)}	\int\:\frac{1}{e^{kx}}dx
y^{''}+y=0,y(0)=0,y(pi)=0	y^{\prime\:\prime\:}+y=0,y(0)=0,y(π)=0
tangent of y=sqrt(2x+1)(4.3)	tangent\:y=\sqrt{2x+1}(4.3)
integral of x(x-1)^5	\int\:x(x-1)^{5}dx
(\partial)/(\partial x)(y^{1/3}x^{2/3})	\frac{\partial\:}{\partial\:x}(y^{\frac{1}{3}}x^{\frac{2}{3}})
integral of 1/((x-1)(x+1))	\int\:\frac{1}{(x-1)(x+1)}dx
derivative of f(x)=x^3-2x^2-4x-6	derivative\:f(x)=x^{3}-2x^{2}-4x-6
integral of (2x+5)e^{2x+5}	\int\:(2x+5)e^{2x+5}dx
derivative of-9/2 x^2+3x+3	derivative\:-\frac{9}{2}x^{2}+3x+3
derivative of (x^2+3/(x^2+5))	\frac{d}{dx}(\frac{x^{2}+3}{x^{2}+5})
integral of cos^3(xsi)n^2x	\int\:\cos^{3}(xsi)n^{2}xdx
(\partial)/(\partial x)(sqrt(-3*x^2)+28)	\frac{\partial\:}{\partial\:x}(\sqrt{-3\cdot\:x^{2}}+28)
integral of 2e^{x/2}x^3	\int\:2e^{\frac{x}{2}}x^{3}dx
(\partial)/(\partial x)(e^{-r(x-ct)^2})	\frac{\partial\:}{\partial\:x}(e^{-r(x-ct)^{2}})
derivative of (3-5x-x^2/(x^2-6))	\frac{d}{dx}(\frac{3-5x-x^{2}}{x^{2}-6})
limit as x approaches 0 of x/(x^2-5x)	\lim\:_{x\to\:0}(\frac{x}{x^{2}-5x})
limit as x approaches infinity+of x^2	\lim\:_{x\to\:\infty\:+}(x^{2})
slope of y=x^2-2x-4	slope\:y=x^{2}-2x-4
derivative of cos(x^3)	derivative\:\cos(x^{3})
(\partial)/(\partial z)(x*ln(y-z))	\frac{\partial\:}{\partial\:z}(x\cdot\:\ln(y-z))
slope of-9/2 x^2+3x+3	slope\:-\frac{9}{2}x^{2}+3x+3
y^{''}-y^'-2y=6e^{2t}	y^{\prime\:\prime\:}-y^{\prime\:}-2y=6e^{2t}
integral of sin^3(xco)s^6x	\int\:\sin^{3}(xco)s^{6}xdx
laplacetransform e^{-2t}cos(t)	laplacetransform\:e^{-2t}\cos(t)
integral of 7/(x+3)	\int\:\frac{7}{x+3}dx
integral of (sin(x))^5cos(x)	\int\:(\sin(x))^{5}\cos(x)dx
derivative of f(x)=14x^{1/7}	derivative\:f(x)=14x^{\frac{1}{7}}
derivative of arccsc(-9x^2)	\frac{d}{dx}(\arccsc(-9x^{2}))
taylor 8xe^x	taylor\:8xe^{x}
slope ofintercept (1,1),(-1,2)	slopeintercept\:(1,1),(-1,2)
integral of x^5e^{x^3}	\int\:x^{5}e^{x^{3}}dx
integral of 3x(x^2-2x)	\int\:3x(x^{2}-2x)dx
derivative of f(x)= 9/(sqrt(x+1))	derivative\:f(x)=\frac{9}{\sqrt{x+1}}
(dy)/(dt)=-3y+9	\frac{dy}{dt}=-3y+9

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