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Popular Calculus Problems

derivative of y= 1/(x-2)	derivative\:y=\frac{1}{x-2}
implicit (dy)/(dx),e^{(9xy)}=10x	implicit\:\frac{dy}{dx},e^{(9xy)}=10x
integral of 1/2 cos(2x)	\int\:\frac{1}{2}\cos(2x)dx
e^y(dy)/(dx)=2x	e^{y}\frac{dy}{dx}=2x
integral of 20y	\int\:20ydy
derivative of ln(arcsin(2x))	\frac{d}{dx}(\ln(\arcsin(2x)))
derivative of (tan(x)/(cos(x)))	\frac{d}{dx}(\frac{\tan(x)}{\cos(x)})
integral of x^2cos((x^3)/5)	\int\:x^{2}\cos(\frac{x^{3}}{5})dx
derivative of 3sec^2(3x)	\frac{d}{dx}(3\sec^{2}(3x))
derivative of x/(x^2+1)	derivative\:\frac{x}{x^{2}+1}
integral of (5+cot^2(x))	\int\:(5+\cot^{2}(x))dx
inverse oflaplace s/(s^2+2s)	inverselaplace\:\frac{s}{s^{2}+2s}
limit as x approaches infinity of 5+3/x	\lim\:_{x\to\:\infty\:}(5+\frac{3}{x})
integral of \sqrt[3]{3-4x^2}(-8x)	\int\:\sqrt[3]{3-4x^{2}}(-8x)dx
integral of 15tan^2(xse)c^3x	\int\:15\tan^{2}(xse)c^{3}x
derivative of xsin(x/2)	\frac{d}{dx}(x\sin(\frac{x}{2}))
sum from n=0 to infinity of n*sin(1/n)	\sum\:_{n=0}^{\infty\:}n\cdot\:\sin(\frac{1}{n})
(\partial)/(\partial x)(sec^2(xy))	\frac{\partial\:}{\partial\:x}(\sec^{2}(xy))
sum from n=1 to infinity of 3/(pi^n)	\sum\:_{n=1}^{\infty\:}\frac{3}{π^{n}}
derivative of x^{1/3}-x^{-2/3}	derivative\:x^{\frac{1}{3}}-x^{-\frac{2}{3}}
limit as x approaches+0 of 2x^2cos(5/x)	\lim\:_{x\to\:+0}(2x^{2}\cos(\frac{5}{x}))
(\partial)/(\partial x)(e^x-2-cos(xy))	\frac{\partial\:}{\partial\:x}(e^{x}-2-\cos(xy))
derivative of 3/(5+x)	\frac{d}{dx}(\frac{3}{5+x})
integral of 1/(sqrt(x)+4)	\int\:\frac{1}{\sqrt{x}+4}dx
y^'=(2cos(y))/(sin(y))	y^{\prime\:}=\frac{2\cos(y)}{\sin(y)}
derivative of (4x^2-x/(x^2+2))	\frac{d}{dx}(\frac{4x^{2}-x}{x^{2}+2})
derivative of (6x^2+2x+2)/(sqrt(x))	derivative\:\frac{6x^{2}+2x+2}{\sqrt{x}}
limit as x approaches 0-of (x-1)/x	\lim\:_{x\to\:0-}(\frac{x-1}{x})
integral of (cos(2x))/(1+sin^2(2x))	\int\:\frac{\cos(2x)}{1+\sin^{2}(2x)}dx
limit as x approaches 0 of (cos(x^2))/(x^2)	\lim\:_{x\to\:0}(\frac{\cos(x^{2})}{x^{2}})
y^'=6+t-y	y^{\prime\:}=6+t-y
derivative of \sqrt[3]{(3x)/(9x-8)}	derivative\:\sqrt[3]{\frac{3x}{9x-8}}
integral of sin^8(x)cos^3(x)	\int\:\sin^{8}(x)\cos^{3}(x)dx
integral from-infinity to 0 of 4^x	\int\:_{-\infty\:}^{0}4^{x}dx
derivative of y=x*e^x	derivative\:y=x\cdot\:e^{x}
integral of (15)/(1-cos(3x))	\int\:\frac{15}{1-\cos(3x)}dx
derivative of 357x+45(x+1/x ^3)	\frac{d}{dx}(357x+45(x+\frac{1}{x})^{3})
laplacetransform (t-1)(3(t-1)^2+9(t-1)+3)	laplacetransform\:(t-1)(3(t-1)^{2}+9(t-1)+3)
integral of 1/(sec(y))	\int\:\frac{1}{\sec(y)}dy
limit as x approaches 0 of x(sin(1/x))	\lim\:_{x\to\:0}(x(\sin(\frac{1}{x})))
(d^2)/(dx^2)(x/(x+4))	\frac{d^{2}}{dx^{2}}(\frac{x}{x+4})
(\partial)/(\partial x)(ln(y^2+x^2))	\frac{\partial\:}{\partial\:x}(\ln(y^{2}+x^{2}))
sum from n=0 to infinity of (2n)/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{2n}{2^{n}}
integral of 1 (e^{x^2}y)	\int\:\frac{d}{1}(e^{x^{2}}y)dx
(dy)/(dx)=-5+x+y	\frac{dy}{dx}=-5+x+y
derivative of \sqrt[3]{7x^4+8x^3}	derivative\:\sqrt[3]{7x^{4}+8x^{3}}
derivative of (200)/(0.9+0.1e^{2h)}	derivative\:\frac{200}{0.9+0.1e^{2h}}
integral of (sqrt(1/z-x^2))/(x^2)	\int\:\frac{\sqrt{\frac{1}{z}-x^{2}}}{x^{2}}dx
integral of (sec^2(θ)-sin(θ))	\int\:(\sec^{2}(θ)-\sin(θ))dθ
integral of-3t^2cos(t)	\int\:-3t^{2}\cos(t)dt
sum from n=1 to infinity of (-3)/(2^n)	\sum\:_{n=1}^{\infty\:}\frac{-3}{2^{n}}
area x,x^2,-x+1	area\:x,x^{2},-x+1
derivative of ln(sqrt((x-1/(x+1))))	\frac{d}{dx}(\ln(\sqrt{\frac{x-1}{x+1}}))
(\partial)/(\partial x)(m/(x^ay^bz^c))	\frac{\partial\:}{\partial\:x}(\frac{m}{x^{a}y^{b}z^{c}})
(\partial)/(\partial x)(3/8 xy)	\frac{\partial\:}{\partial\:x}(\frac{3}{8}xy)
integral of t^2e^{-(s-1)t}	\int\:t^{2}e^{-(s-1)t}dt
derivative of acos(bx+c+d)	\frac{d}{dx}(a\cos(bx+c)+d)
area 6x^2-2x,x^3-6x+3	area\:6x^{2}-2x,x^{3}-6x+3
integral of (2^0-3^0)^x	\int\:(2^{0}-3^{0})^{x}dx
f(x)=sqrt(3x+1)	f(x)=\sqrt{3x+1}
(2x-1)dx+(5y+9)dy=0	(2x-1)dx+(5y+9)dy=0
(\partial)/(\partial x)(2x^2+3y^2-4x-5)	\frac{\partial\:}{\partial\:x}(2x^{2}+3y^{2}-4x-5)
derivative of (x^2+5^5)	\frac{d}{dx}((x^{2}+5)^{5})
derivative of (x^2+6/x)	\frac{d}{dx}(\frac{x^{2}+6}{x})
derivative of (x^2+4x/((3x^3+2)^4))	\frac{d}{dx}(\frac{x^{2}+4x}{(3x^{3}+2)^{4}})
y^'=(4+3x)^4	y^{\prime\:}=(4+3x)^{4}
integral of (x+9)ln(x)	\int\:(x+9)\ln(x)dx
taylor 1/(x^2+1),0	taylor\:\frac{1}{x^{2}+1},0
derivative of (x^7/7+(2x)/3)	\frac{d}{dx}(\frac{x^{7}}{7}+\frac{2x}{3})
derivative of f(x)=(2x-5)^4(x^2+x+1)^5	derivative\:f(x)=(2x-5)^{4}(x^{2}+x+1)^{5}
integral of (t^2+2t+1)^4	\int\:(t^{2}+2t+1)^{4}dt
25y^{''}+3y=0	25y^{\prime\:\prime\:}+3y=0
integral from 0 to 4 of 2pix(8-x^{3/2})	\int\:_{0}^{4}2πx(8-x^{\frac{3}{2}})dx
integral from 2 to 3 of (33)/(sqrt(3-x))	\int\:_{2}^{3}\frac{33}{\sqrt{3-x}}dx
laplacetransform cos^2(16t)	laplacetransform\:\cos^{2}(16t)
integral of (x+1)sin(x^2+2x+3)	\int\:(x+1)\sin(x^{2}+2x+3)dx
(dx)/(dt)=e^x*sin(t)	\frac{dx}{dt}=e^{x}\cdot\:\sin(t)
maclaurin sin((xpi)/4)	maclaurin\:\sin(\frac{xπ}{4})
(x^{-1/2})^'	(x^{-\frac{1}{2}})^{\prime\:}
limit as x approaches infinity of 1/0	\lim\:_{x\to\:\infty\:}(\frac{1}{0})
limit as x approaches 3 of-x^2+x-3	\lim\:_{x\to\:3}(-x^{2}+x-3)
integral from-infinity to 0 of x/(x^4+9)	\int\:_{-\infty\:}^{0}\frac{x}{x^{4}+9}dx
integral of (x^2)/(sqrt(100-x^2))	\int\:\frac{x^{2}}{\sqrt{100-x^{2}}}dx
limit as x approaches-7 of (7-x)/(7+x)	\lim\:_{x\to\:-7}(\frac{7-x}{7+x})
laplacetransform te^{-3t}cos(5t)	laplacetransform\:te^{-3t}\cos(5t)
(y+x)(dy)/(dx)=x-y	(y+x)\frac{dy}{dx}=x-y
(\partial)/(\partial x)(ln(x+y+z))	\frac{\partial\:}{\partial\:x}(\ln(x+y+z))
f(x)= 1/2 e^{2x}	f(x)=\frac{1}{2}e^{2x}
integral of x^2-3x+2	\int\:x^{2}-3x+2dx
integral of ((x^2-x+5))/x	\int\:\frac{(x^{2}-x+5)}{x}dx
derivative of sqrt(1+2x^2)	\frac{d}{dx}(\sqrt{1+2x^{2}})
y^{''}-5/x y^'+8/(x^2)y=0	y^{\prime\:\prime\:}-\frac{5}{x}y^{\prime\:}+\frac{8}{x^{2}}y=0
7t(dy)/(dt)-3y=sqrt(t)	7t\frac{dy}{dt}-3y=\sqrt{t}
slope of y=4-x^2,(3,-5)	slope\:y=4-x^{2},(3,-5)
derivative of 3/((4x^2-1^4))	\frac{d}{dx}(\frac{3}{(4x^{2}-1)^{4}})
derivative of sqrt(x^3)+6/7 x-10	\frac{d}{dx}(\sqrt{x^{3}}+\frac{6}{7}x-10)
integral of 7tan^3(2x)sec^5(2x)	\int\:7\tan^{3}(2x)\sec^{5}(2x)dx
integral from 1 to 2 of 5e^{1/x}	\int\:_{1}^{2}5e^{\frac{1}{x}}dx
inverse oflaplace (20)/((s^2+4)(s-4))	inverselaplace\:\frac{20}{(s^{2}+4)(s-4)}
integral of (a^2*x)^{((1-a))/a}	\int\:(a^{2}\cdot\:x)^{\frac{(1-a)}{a}}dx

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