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Popular Calculus Problems

derivative of 5+4x-x^3	\frac{d}{dx}(5+4x-x^{3})
area x^2-1,-1,6	area\:x^{2}-1,-1,6
derivative of y=(5x^4-3x^3)(3x^2-7x^3)	derivative\:y=(5x^{4}-3x^{3})(3x^{2}-7x^{3})
integral of (3z^2)/y	\int\:\frac{3z^{2}}{y}dy
tangent of-5x^3-1	tangent\:-5x^{3}-1
integral of 2cos(sqrt(x))	\int\:2\cos(\sqrt{x})dx
y^'+5y=0	y^{\prime\:}+5y=0
derivative of x^3e^{1/3 x}+(2x/(5+x))	\frac{d}{dx}(x^{3}e^{\frac{1}{3}x}+\frac{2x}{5+x})
integral of 1/(sqrt(1-4x-x^2))	\int\:\frac{1}{\sqrt{1-4x-x^{2}}}dx
derivative of x^{7/8}	\frac{d}{dx}(x^{\frac{7}{8}})
integral of (csc^2(x)-a^x)	\int\:(\csc^{2}(x)-a^{x})dx
limit as x approaches infinity of 0^{-x}	\lim\:_{x\to\:\infty\:}(0^{-x})
y^{''}-2y^'+1y=0,y(0)=5,y^'(0)=4	y^{\prime\:\prime\:}-2y^{\prime\:}+1y=0,y(0)=5,y^{\prime\:}(0)=4
derivative of ln(x-9)	derivative\:\ln(x-9)
(\partial)/(\partial x)((x+1)^2(x^2+2x))	\frac{\partial\:}{\partial\:x}((x+1)^{2}(x^{2}+2x))
derivative of f(x)=(x^3-1x^2+2)/(x^2)	derivative\:f(x)=\frac{x^{3}-1x^{2}+2}{x^{2}}
integral of (xsqrt(x+3))	\int\:(x\sqrt{x+3})dx
(\partial)/(\partial x)(x^4+y^4+3x^2y^3)	\frac{\partial\:}{\partial\:x}(x^{4}+y^{4}+3x^{2}y^{3})
area 13+2x-x^2,3x+1	area\:13+2x-x^{2},3x+1
derivative of f(x)=(x+1)^{2x}	derivative\:f(x)=(x+1)^{2x}
roots x/a	roots\:\frac{x}{a}
tangent of x/y =sin((pixy)/2),(1,1)	tangent\:\frac{x}{y}=\sin(\frac{πxy}{2}),(1,1)
(\partial)/(\partial x)(y^2+2xy-x^2)	\frac{\partial\:}{\partial\:x}(y^{2}+2xy-x^{2})
limit as x approaches 16 of x+2sqrt(x)	\lim\:_{x\to\:16}(x+2\sqrt{x})
derivative of y=x*sqrt(x)	derivative\:y=x\cdot\:\sqrt{x}
tangent of y=4x-3x^2(2-4)	tangent\:y=4x-3x^{2}(2-4)
3xy^3dx-(x+2)dy=0	3xy^{3}dx-(x+2)dy=0
derivative of 2cos^2(2x)	\frac{d}{dx}(2\cos^{2}(2x))
limit as x approaches 3-of (3x+2)/(x-3)	\lim\:_{x\to\:3-}(\frac{3x+2}{x-3})
tangent of f(x)= 1/(3-2x),\at x=-1	tangent\:f(x)=\frac{1}{3-2x},\at\:x=-1
(\partial)/(\partial x)(3/(3x+y))	\frac{\partial\:}{\partial\:x}(\frac{3}{3x+y})
integral of-1/2 y	\int\:-\frac{1}{2}ydy
limit as x approaches-1 of x+3	\lim\:_{x\to\:-1}(x+3)
inverse oflaplace (0.6)/(s+2)	inverselaplace\:\frac{0.6}{s+2}
(dy)/(dx)=((x^2y-y))/((y+1)),y(0)=1	\frac{dy}{dx}=\frac{(x^{2}y-y)}{(y+1)},y(0)=1
integral of e^{sqrt(u)}	\int\:e^{\sqrt{u}}du
integral of ((sqrt(x)-1)^3)/(2sqrt(x))	\int\:\frac{(\sqrt{x}-1)^{3}}{2\sqrt{x}}dx
integral of 4x^3(x^4+5)^6	\int\:4x^{3}(x^{4}+5)^{6}dx
limit as x approaches+1+of sqrt(1-x^2)	\lim\:_{x\to\:+1+}(\sqrt{1-x^{2}})
integral of (arctan(7x))/(1+49x^2)	\int\:\frac{\arctan(7x)}{1+49x^{2}}dx
limit as x approaches pi/3 of 1-2cos(x)	\lim\:_{x\to\:\frac{π}{3}}(1-2\cos(x))
tangent of 5/x ,\at x=4	tangent\:\frac{5}{x},\at\:x=4
(dy)/(dx)=(3x+2y+1)/(3x+2y-1)	\frac{dy}{dx}=\frac{3x+2y+1}{3x+2y-1}
derivative of f(x)=(4x^2-8x+8)e^x	derivative\:f(x)=(4x^{2}-8x+8)e^{x}
(\partial)/(\partial y)(xe^{2y}sin(7z))	\frac{\partial\:}{\partial\:y}(xe^{2y}\sin(7z))
integral from-8 to 64 of 1/(\sqrt[3]{x)}	\int\:_{-8}^{64}\frac{1}{\sqrt[3]{x}}dx
derivative of 24x-0.01x^2	derivative\:24x-0.01x^{2}
y^{''}+121y=sec(11x)	y^{\prime\:\prime\:}+121y=\sec(11x)
limit as x approaches 0-of (1-e^{-3x})/x	\lim\:_{x\to\:0-}(\frac{1-e^{-3x}}{x})
derivative of (e^x/(7x^2+8))	\frac{d}{dx}(\frac{e^{x}}{7x^{2}+8})
integral from 0 to 5 of \|x-3\|	\int\:_{0}^{5}\left\|x-3\right\|dx
integral of x13^x	\int\:x13^{x}dx
integral of y^2sinh(5y)	\int\:y^{2}\sinh(5y)dy
integral from 0 to 1 of integral from 0 to sqrt(x of)(4-2y)/((1+x)^2)	\int\:_{0}^{1}\int\:_{0}^{\sqrt{x}}\frac{4-2y}{(1+x)^{2}}dydx
integral from 0 to pi/(24) of cos(6x)	\int\:_{0}^{\frac{π}{24}}\cos(6x)dx
(\partial)/(\partial z)(3ye^{-z})	\frac{\partial\:}{\partial\:z}(3ye^{-z})
(dy)/(dx)=(((2y+3))/(4x+5))^2	\frac{dy}{dx}=(\frac{(2y+3)}{4x+5})^{2}
derivative of ln(sqrt((3x+1/(x^2-2))))	\frac{d}{dx}(\ln(\sqrt{\frac{3x+1}{x^{2}-2}}))
derivative of 3xe^xcsc(x)	derivative\:3xe^{x}\csc(x)
limit as x approaches 0 of sin^2(x)(1/x)	\lim\:_{x\to\:0}(\sin^{2}(x)(\frac{1}{x}))
limit as x approaches-1 of 1/(x^2+1)	\lim\:_{x\to\:-1}(\frac{1}{x^{2}+1})
sum from n=0 to infinity of 6/(5^n)	\sum\:_{n=0}^{\infty\:}\frac{6}{5^{n}}
integral of 2sec(2x)tan(2x)	\int\:2\sec(2x)\tan(2x)dx
y^'+(1/x)y=8x^2	y^{\prime\:}+(\frac{1}{x})y=8x^{2}
integral from 2 to 4 of x^2y+y^2x+x+y	\int\:_{2}^{4}x^{2}y+y^{2}x+x+ydx
taylor 1/(1+x^{-1)}	taylor\:\frac{1}{1+x^{-1}}
y^{''}-5y^'=0,y(0)=6,y^'(0)=-9	y^{\prime\:\prime\:}-5y^{\prime\:}=0,y(0)=6,y^{\prime\:}(0)=-9
(\partial)/(\partial x)(ln(x^4-y^4))	\frac{\partial\:}{\partial\:x}(\ln(x^{4}-y^{4}))
derivative of In^4x	\frac{d}{dx}(In^{4}x)
derivative of (5x+1)/(5x-1)	derivative\:\frac{5x+1}{5x-1}
area y=sqrt(x),y=x^6	area\:y=\sqrt{x},y=x^{6}
y^'+(2y)/x =4x	y^{\prime\:}+\frac{2y}{x}=4x
integral of 1/(4-(x+1)^2)	\int\:\frac{1}{4-(x+1)^{2}}dx
12(t+1)(dy)/(dt)-9y=27t	12(t+1)\frac{dy}{dt}-9y=27t
derivative of cos(4)x^3	derivative\:\cos(4)x^{3}
derivative of 4xy^2-xy^3-x^2y^2	\frac{d}{dx}(4xy^{2}-xy^{3}-x^{2}y^{2})
derivative of cot^2(pix)	derivative\:\cot^{2}(πx)
derivative of 8(2ze^z+e^zz^2)	derivative\:8(2ze^{z}+e^{z}z^{2})
(dy)/(dx)=-4xy^2	\frac{dy}{dx}=-4xy^{2}
limit as x approaches-3 of x+1	\lim\:_{x\to\:-3}(x+1)
area sqrt(x+2), 1/(x+1),x=2	area\:\sqrt{x+2},\frac{1}{x+1},x=2
limit as x approaches 0 of (sqrt(e^x))/x	\lim\:_{x\to\:0}(\frac{\sqrt{e^{x}}}{x})
(\partial)/(\partial x)(x^5yz^2+2yz)	\frac{\partial\:}{\partial\:x}(x^{5}yz^{2}+2yz)
derivative of (3x^2-x+1/(x^7))	\frac{d}{dx}(\frac{3x^{2}-x+1}{x^{7}})
integral of 1/(xsqrt(36x^2+1))	\int\:\frac{1}{x\sqrt{36x^{2}+1}}dx
y^'=-y^{1/3}	y^{\prime\:}=-y^{\frac{1}{3}}
derivative of 2sin(sqrt(x)-x)	\frac{d}{dx}(2\sin(\sqrt{x})-x)
slope of (-5/2 ,1),(-1/2 ,4)	slope\:(-\frac{5}{2},1),(-\frac{1}{2},4)
integral of (5x)/2	\int\:\frac{5x}{2}dx
integral of (32x)/(x^4-16)	\int\:\frac{32x}{x^{4}-16}dx
(\partial)/(\partial x)(y^4cos(3x)*3)	\frac{\partial\:}{\partial\:x}(y^{4}\cos(3x)\cdot\:3)
integral of (8x^3)/(x-5)	\int\:\frac{8x^{3}}{x-5}dx
limit as x approaches 0 of ((x+2)^2-4)/x	\lim\:_{x\to\:0}(\frac{(x+2)^{2}-4}{x})
f(x)=xe^x-e^x	f(x)=xe^{x}-e^{x}
integral of 7e^6	\int\:7e^{6}dx
limit as t approaches 1 of 1/(t-1)	\lim\:_{t\to\:1}(\frac{1}{t-1})
limit as x approaches-2 of (4/x+2)/(x+2)	\lim\:_{x\to\:-2}(\frac{\frac{4}{x}+2}{x+2})
tangent of f(x)=(4x-4)^{1/3},\at x=2	tangent\:f(x)=(4x-4)^{\frac{1}{3}},\at\:x=2
f(x)=arctan(e^x)	f(x)=\arctan(e^{x})
x^{''}+x^'+x=0	x^{\prime\:\prime\:}+x^{\prime\:}+x=0

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