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Popular Calculus Problems

(\partial)/(\partial x)(-2xysin(xy^2))	\frac{\partial\:}{\partial\:x}(-2xy\sin(xy^{2}))
tangent of tan^2(x)	tangent\:\tan^{2}(x)
y^'=y-x^2+1,y(0)=0	y^{\prime\:}=y-x^{2}+1,y(0)=0
integral of (b-x)/x	\int\:\frac{b-x}{x}dx
(\partial)/(\partial x)((e^y)/(x+y^3))	\frac{\partial\:}{\partial\:x}(\frac{e^{y}}{x+y^{3}})
limit as x approaches 0 of (x-20)/(x-4)	\lim\:_{x\to\:0}(\frac{x-20}{x-4})
(d^2y)/(dt^2)+2(dy)/(dt)+y=2	\frac{d^{2}y}{dt^{2}}+2\frac{dy}{dt}+y=2
integral of m 1 (v)(v)	\int\:m\frac{d}{1}(v)(v)dx
integral of 1/(a-x)	\int\:\frac{1}{a-x}dx
integral of (x+2)sqrt(4x+x^2)	\int\:(x+2)\sqrt{4x+x^{2}}dx
(\partial)/(\partial z)(2x^2+2yz)	\frac{\partial\:}{\partial\:z}(2x^{2}+2yz)
limit as x approaches-1 of 2x^3-4	\lim\:_{x\to\:-1}(2x^{3}-4)
inverse oflaplace (12)/((3s-5))	inverselaplace\:\frac{12}{(3s-5)}
integral of 1/(n^3)	\int\:\frac{1}{n^{3}}
slope of (-5,-8),(5,2)	slope\:(-5,-8),(5,2)
limit as x approaches infinity of 3+4/x	\lim\:_{x\to\:\infty\:}(3+\frac{4}{x})
derivative of (6-xe^x/(x+e^x))	\frac{d}{dx}(\frac{6-xe^{x}}{x+e^{x}})
integral of (3x^2)/(x^2+7)	\int\:\frac{3x^{2}}{x^{2}+7}dx
derivative of f(x)=(3/(sqrt(x)))	derivative\:f(x)=(\frac{3}{\sqrt{x}})
(4-x)^'	(4-x)^{\prime\:}
integral from 0 to 9 of 9x-x^2	\int\:_{0}^{9}9x-x^{2}dx
limit as x approaches 5 of 3x	\lim\:_{x\to\:5}(3x)
derivative of h(x)=(sqrt(3))/(x^3+1)	derivative\:h(x)=\frac{\sqrt{3}}{x^{3}+1}
9(t+1)(dy)/(dt)-5y=20t	9(t+1)\frac{dy}{dt}-5y=20t
inverse oflaplace (-2e^s)/((s^2-2s-8))	inverselaplace\:\frac{-2e^{s}}{(s^{2}-2s-8)}
limit as x approaches infinity of (x)^x	\lim\:_{x\to\:\infty\:}((x)^{x})
integral of u/(1-u)	\int\:\frac{u}{1-u}du
integral of x^{-3}ln(5x)	\int\:x^{-3}\ln(5x)dx
sum from n=6 to infinity of e^{5-2n}	\sum\:_{n=6}^{\infty\:}e^{5-2n}
integral of 2+1/(1-x)	\int\:2+\frac{1}{1-x}dx
(\partial)/(\partial z)(z)	\frac{\partial\:}{\partial\:z}(z)
derivative of 3/((x-1))	derivative\:\frac{3}{(x-1)}
integral of (e^x-1)/(e^{2x)}	\int\:\frac{e^{x}-1}{e^{2x}}dx
derivative of y=-2x-1	derivative\:y=-2x-1
sum from n=1 to infinity of 1/(n+3^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{n+3^{n}}
derivative of (e^x+1/(e^x-1))	\frac{d}{dx}(\frac{e^{x}+1}{e^{x}-1})
derivative of f(x)=9x^8e^x+e^xx^9	derivative\:f(x)=9x^{8}e^{x}+e^{x}x^{9}
derivative of (5+csc(x)/(9-csc(x)))	\frac{d}{dx}(\frac{5+\csc(x)}{9-\csc(x)})
y^'=x^4-1/x y	y^{\prime\:}=x^{4}-\frac{1}{x}y
integral from 0 to 1 of x^2ln(x)	\int\:_{0}^{1}x^{2}\ln(x)dx
derivative of 1/((1-x^6^{3/2)})	\frac{d}{dx}(\frac{1}{(1-x^{6})^{\frac{3}{2}}})
integral from 0 to N of e^{-st}e^{-3t}	\int\:_{0}^{N}e^{-st}e^{-3t}dt
y^'-(4x-y+1)^2=0	y^{\prime\:}-(4x-y+1)^{2}=0
derivative of 1/0	\frac{d}{dx}(\frac{1}{0})
integral of sin(2)	\int\:\sin(2)dx
(dy}{dx}+\frac{3y)/x+2=3x	\frac{dy}{dx}+\frac{3y}{x}+2=3x
12x^2y+y^'=5x^2	12x^{2}y+y^{\prime\:}=5x^{2}
derivative of f(x)=sqrt(cos(2x))	derivative\:f(x)=\sqrt{\cos(2x)}
integral of (x+2)^{1/2}	\int\:(x+2)^{\frac{1}{2}}dx
integral from 0 to 6 of x^3	\int\:_{0}^{6}x^{3}dx
limit as n approaches infinity of n^{-3}	\lim\:_{n\to\:\infty\:}(n^{-3})
(\partial)/(\partial x)(cos(xy)-1-sin(y))	\frac{\partial\:}{\partial\:x}(\cos(xy)-1-\sin(y))
y^'=-7yln((10)/y)	y^{\prime\:}=-7y\ln(\frac{10}{y})
derivative of x^2+6x-16	\frac{d}{dx}(x^{2}+6x-16)
(\partial)/(\partial h)(pir^2h)	\frac{\partial\:}{\partial\:h}(πr^{2}h)
(\partial)/(\partial x)(sin(x)sin(y))	\frac{\partial\:}{\partial\:x}(\sin(x)\sin(y))
(x*(dy)/(dx)-y)cos(y/x)+x=0	(x\cdot\:\frac{dy}{dx}-y)\cos(\frac{y}{x})+x=0
integral of (x^6+2x^4+6x-9)/(x^3+3)	\int\:\frac{x^{6}+2x^{4}+6x-9}{x^{3}+3}dx
derivative of 6/((1-x)^3)	derivative\:\frac{6}{(1-x)^{3}}
limit as k approaches infinity of (-1)^k	\lim\:_{k\to\:\infty\:}((-1)^{k})
limit as x approaches infinity of 7x^2	\lim\:_{x\to\:\infty\:}(7x^{2})
f^'(x)=(3x^6+4x^3)^4	f^{\prime\:}(x)=(3x^{6}+4x^{3})^{4}
tangent of x^3+8,\at x=-2	tangent\:x^{3}+8,\at\:x=-2
integral of (3x^3-5x^2+10x-3)/(3x+1)	\int\:\frac{3x^{3}-5x^{2}+10x-3}{3x+1}dx
(\partial)/(\partial y)(x*y)	\frac{\partial\:}{\partial\:y}(x\cdot\:y)
laplacetransform (2(t-2)^2)+10(t-2)+15	laplacetransform\:(2(t-2)^{2})+10(t-2)+15
integral of 1/(x(ln(x))^8)	\int\:\frac{1}{x(\ln(x))^{8}}dx
integral of (2+x+sqrt(x))/x	\int\:\frac{2+x+\sqrt{x}}{x}dx
(sec(x))^'	(\sec(x))^{\prime\:}
derivative of 0.334*sin(0.3494x-0.06988)	derivative\:0.334\cdot\:\sin(0.3494x-0.06988)
derivative of sqrt(6+sec(pix^2))	\frac{d}{dx}(\sqrt{6+\sec(π)x^{2}})
area sin(x),[0,pi]	area\:\sin(x),[0,π]
integral of e^{cos(3t)}sin(3t)	\int\:e^{\cos(3t)}\sin(3t)dt
y^{''}+2y^'+12y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+12y=0,y(0)=1,y^{\prime\:}(0)=0
limit as x approaches 1-of 3x^2-4x+4	\lim\:_{x\to\:1-}(3x^{2}-4x+4)
integral of (ln(x+1))/(x+1)	\int\:\frac{\ln(x+1)}{x+1}dx
y^'=y(y-3),y(0)=a	y^{\prime\:}=y(y-3),y(0)=a
sum from n=0 to infinity of (nx^n)/(n+2)	\sum\:_{n=0}^{\infty\:}\frac{nx^{n}}{n+2}
f(x)=5^{x^2}	f(x)=5^{x^{2}}
(\partial)/(\partial y)(1/(x+y))	\frac{\partial\:}{\partial\:y}(\frac{1}{x+y})
(dy)/(dx)=-((x+6))/(7y^2)	\frac{dy}{dx}=-\frac{(x+6)}{7y^{2}}
(dθ)/(dt)=40-2/5 (θ-15)	\frac{dθ}{dt}=40-\frac{2}{5}(θ-15)
y^{''}+4y^'=0,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}+4y^{\prime\:}=0,y(0)=1,y^{\prime\:}(0)=1
derivative of f(x)=(9x^2-15x)e^x	derivative\:f(x)=(9x^{2}-15x)e^{x}
integral of sin(x)cos(x)ln(sin(x))	\int\:\sin(x)\cos(x)\ln(\sin(x))dx
y^{''}-3y^'+2y=0,y(0)=1,y^'(0)=-7/3	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=0,y(0)=1,y^{\prime\:}(0)=-\frac{7}{3}
integral from 0 to 1 of sqrt(4-x^2)	\int\:_{0}^{1}\sqrt{4-x^{2}}dx
integral of 9/(x^4)	\int\:\frac{9}{x^{4}}dx
tangent of y=(sqrt(x))/(x+1),(4, 2/5)	tangent\:y=\frac{\sqrt{x}}{x+1},(4,\frac{2}{5})
limit as x approaches 0 of cos(x^2)	\lim\:_{x\to\:0}(\cos(x^{2}))
area 7x-x^2,2x	area\:7x-x^{2},2x
derivative of f(x)= 1/2 (x+1)^{-1/2}	derivative\:f(x)=\frac{1}{2}(x+1)^{-\frac{1}{2}}
sum from n=1 to infinity of (1/5)^n	\sum\:_{n=1}^{\infty\:}(\frac{1}{5})^{n}
derivative of (x+1/(2-x))	\frac{d}{dx}(\frac{x+1}{2-x})
u'(x)	u\prime\:(x)
derivative of e^{cos(3x)}	derivative\:e^{\cos(3x)}
limit as x approaches-3 of-3/(x+3)	\lim\:_{x\to\:-3}(-\frac{3}{x+3})
derivative of x^4	derivative\:x^{4}
y^{''}+4y^'-y=0	y^{\prime\:\prime\:}+4y^{\prime\:}-y=0
integral from 0 to 2pi of sin^2(10x)	\int\:_{0}^{2π}\sin^{2}(10x)dx

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