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Popular Calculus Problems

derivative of 1+(3/2 x^{(1/2})^2)	\frac{d}{dx}(1+(\frac{3}{2}x^{(\frac{1}{2})})^{2})
tangent of f(x)=20x-16x^2,\at x=3	tangent\:f(x)=20x-16x^{2},\at\:x=3
y^'+2/(t+1)y=3t	y^{\prime\:}+\frac{2}{t+1}y=3t
(\partial)/(\partial x)(v/(2u+v))	\frac{\partial\:}{\partial\:x}(\frac{v}{2u+v})
derivative of 3e^{-3x}	\frac{d}{dx}(3e^{-3x})
derivative of 9klog_{e}(((x+9)/(x-9)))	\frac{d}{dx}(9k\log_{e}(\frac{(x+9)}{x-9}))
inverse oflaplace (5s+50.1)/((s+5)^2-5)	inverselaplace\:\frac{5s+50.1}{(s+5)^{2}-5}
sum from k=0 to infinity of (k-1)/(2^{k+1)}	\sum\:_{k=0}^{\infty\:}\frac{k-1}{2^{k+1}}
limit as (x,y) approaches (1,2) of 1+x+y	\lim\:_{(x,y)\to\:(1,2)}(1+x+y)
f(x)=x^3-5+2x	f(x)=x^{3}-5+2x
limit as x approaches infinity of e^{-x}	\lim\:_{x\to\:\infty\:}(e^{-x})
(\partial)/(\partial x)((2x-3)/(xy))	\frac{\partial\:}{\partial\:x}(\frac{2x-3}{xy})
derivative of sqrt(7-3u)	derivative\:\sqrt{7-3u}
(\partial)/(\partial y)(x^2y+3y+x^2y^3-4x)	\frac{\partial\:}{\partial\:y}(x^{2}y+3y+x^{2}y^{3}-4x)
y^{''}+y^'-2y=2t,y(0)=0,y^'(0)=7	y^{\prime\:\prime\:}+y^{\prime\:}-2y=2t,y(0)=0,y^{\prime\:}(0)=7
tangent of y=x^3-2x+2(2.6)	tangent\:y=x^{3}-2x+2(2.6)
derivative of x+2/(sin(x))	\frac{d}{dx}(x+\frac{2}{\sin(x)})
integral from 0 to pi/2 of 24x^2sin(x)	\int\:_{0}^{\frac{π}{2}}24x^{2}\sin(x)dx
limit as x approaches 0-of 3/(x^2-x)	\lim\:_{x\to\:0-}(\frac{3}{x^{2}-x})
integral of (-x-8)/(x^2+9)	\int\:\frac{-x-8}{x^{2}+9}dx
derivative of 2x^2-2x	derivative\:2x^{2}-2x
integral of 15arctan(x)	\int\:15\arctan(x)dx
integral of (ln(x^{14}))/x	\int\:\frac{\ln(x^{14})}{x}dx
(\partial)/(\partial x)(-y^3-x)	\frac{\partial\:}{\partial\:x}(-y^{3}-x)
integral of sin^3(x/2)cos(x/2)	\int\:\sin^{3}(\frac{x}{2})\cos(\frac{x}{2})dx
inverse oflaplace (e^{-3s})/(s^2+6s+13)	inverselaplace\:\frac{e^{-3s}}{s^{2}+6s+13}
derivative of f(x)=13	derivative\:f(x)=13
integral of (1+u)/(-2u-1-u^2)	\int\:\frac{1+u}{-2u-1-u^{2}}du
laplacetransform e^{-t}cos^2(t)	laplacetransform\:e^{-t}\cos^{2}(t)
integral of (x^2+8x-3)/(x^3+3x)	\int\:\frac{x^{2}+8x-3}{x^{3}+3x}dx
y^{''}+5y^'+6y=108x^2	y^{\prime\:\prime\:}+5y^{\prime\:}+6y=108x^{2}
integral from 7 to infinity of (ln(x))/x	\int\:_{7}^{\infty\:}\frac{\ln(x)}{x}dx
integral from 1 to 2 of (x^2)	\int\:_{1}^{2}(x^{2})dx
integral of (\sqrt[9]{x})	\int\:(\sqrt[9]{x})dx
integral of 9x^{-3}	\int\:9x^{-3}dx
derivative of (2x/(7x^2+1))	\frac{d}{dx}(\frac{2x}{7x^{2}+1})
y^{''}+256y=sec(16x)	y^{\prime\:\prime\:}+256y=\sec(16x)
tangent of y=12(x-1/x)^2,\at x=2	tangent\:y=12(x-\frac{1}{x})^{2},\at\:x=2
derivative of y=4xcos(x^2)	derivative\:y=4x\cos(x^{2})
integral of (2e^{9x})	\int\:(2e^{9x})dx
derivative of ((x-1)/((x-2)))	\frac{d}{dx}(\frac{(x-1)}{(x-2)})
integral of x^5e^{3x}	\int\:x^{5}e^{3x}dx
derivative of f(x)=(x+3)^2	derivative\:f(x)=(x+3)^{2}
integral from 1/2 to 1 of (x^{-3}-2)	\int\:_{\frac{1}{2}}^{1}(x^{-3}-2)dx
tangent of y=6xe^x,(0,0)	tangent\:y=6xe^{x},(0,0)
derivative of cos(4t)	derivative\:\cos(4t)
(\partial)/(\partial x)(e^{-y}(x+e^y))	\frac{\partial\:}{\partial\:x}(e^{-y}(x+e^{y}))
area y=x^2,y=2	area\:y=x^{2},y=2
3x^2y^'=y^'+6xe^{-y}	3x^{2}y^{\prime\:}=y^{\prime\:}+6xe^{-y}
derivative of (e^{4x^2})^7	derivative\:(e^{4x^{2}})^{7}
(dx)/(dt)=5x-3	\frac{dx}{dt}=5x-3
derivative of 12x	derivative\:12x
y^'=e^{3y}sin(4x)	y^{\prime\:}=e^{3y}\sin(4x)
(\partial)/(\partial x)(sqrt(6-x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{6-x^{2}-y^{2}})
tangent of f(x)=x^2+x,\at x=1,x=4	tangent\:f(x)=x^{2}+x,\at\:x=1,x=4
tangent of f(x)=x^3-5x^2	tangent\:f(x)=x^{3}-5x^{2}
integral from-2 to 0 of x^2e^{x^3+8}	\int\:_{-2}^{0}x^{2}e^{x^{3}+8}dx
integral of 2/(1+cos(2x))	\int\:\frac{2}{1+\cos(2x)}dx
integral of (x-1)(x+1)	\int\:(x-1)(x+1)dx
integral of x^3(2x^4+4)^2	\int\:x^{3}(2x^{4}+4)^{2}dx
integral of (arctan(x))/(x^2+1)	\int\:\frac{\arctan(x)}{x^{2}+1}dx
taylor e^x,2	taylor\:e^{x},2
integral of (ax+b)/(cx+	\int\:\frac{ax+b}{cx+d}dx
derivative of (4x^{3/2}/x)	\frac{d}{dx}(\frac{4x^{\frac{3}{2}}}{x})
integral of 10x-3x^2-x^3	\int\:10x-3x^{2}-x^{3}dx
x((dy)/(dx))+2y=0	x(\frac{dy}{dx})+2y=0
integral of (x^2-x)cos(x)	\int\:(x^{2}-x)\cos(x)dx
limit as x approaches 5-of 2/((x-5))	\lim\:_{x\to\:5-}(\frac{2}{(x-5)})
derivative of 3x^2e^x+e^x(x^3+5)	derivative\:3x^{2}e^{x}+e^{x}(x^{3}+5)
ye^{2x}dx-(4+e^{2x})dy=0	ye^{2x}dx-(4+e^{2x})dy=0
integral from 0 to 2pi of cos^4(x)	\int\:_{0}^{2π}\cos^{4}(x)dx
integral from 0 to pi/(20) of cos(10x)	\int\:_{0}^{\frac{π}{20}}\cos(10x)dx
sum from n=1 to infinity of (2^n)/n	\sum\:_{n=1}^{\infty\:}\frac{2^{n}}{n}
derivative of (x^2+x+1/(x^2+1))	\frac{d}{dx}(\frac{x^{2}+x+1}{x^{2}+1})
derivative of 1/2 (tan(x-x))	\frac{d}{dx}(\frac{1}{2}(\tan(x)-x))
sum from n=0 to infinity of n^3x^n	\sum\:_{n=0}^{\infty\:}n^{3}x^{n}
derivative of 9xarcsin(x)	\frac{d}{dx}(9x\arcsin(x))
derivative of sqrt(6x-5)	\frac{d}{dx}(\sqrt{6x-5})
integral of (x^3-2x+3)/(x-1)	\int\:\frac{x^{3}-2x+3}{x-1}dx
inverse oflaplace 1/((s+4)^2)	inverselaplace\:\frac{1}{(s+4)^{2}}
y^{''}-2y^'+y=t+1,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}-2y^{\prime\:}+y=t+1,y(0)=0,y^{\prime\:}(0)=0
derivative of 5^{x+1}	\frac{d}{dx}(5^{x+1})
tangent of-3x^2	tangent\:-3x^{2}
derivative of 4/(4x+1)	\frac{d}{dx}(\frac{4}{4x+1})
integral of (4+8x)/(1+x^2)	\int\:\frac{4+8x}{1+x^{2}}dx
integral of 9x^2+4x-3	\int\:9x^{2}+4x-3dx
derivative of (2x-x^2/(sqrt(x))-3cot(x))	\frac{d}{dx}(\frac{2x-x^{2}}{\sqrt{x}}-3\cot(x))
limit as x approaches 4 of 2x^2+7	\lim\:_{x\to\:4}(2x^{2}+7)
(dh}{dt}=\frac{(7-e^{-t/5}))/6-2/9 h	\frac{dh}{dt}=\frac{(7-e^{-\frac{t}{5}})}{6}-\frac{2}{9}h
slope of 2xy^3=xy+6	slope\:2xy^{3}=xy+6
integral of sqrt(1/(4x)+9)	\int\:\sqrt{\frac{1}{4x}+9}dx
y^'=((x^4+x^2y^2+y^4))/(x^3y)	y^{\prime\:}=\frac{(x^{4}+x^{2}y^{2}+y^{4})}{x^{3}y}
laplacetransform t-2	laplacetransform\:t-2
derivative of y=log_{6}(x)	derivative\:y=\log_{6}(x)
limit as x approaches 2 of x^2	\lim\:_{x\to\:2}(x^{2})
integral of (sqrt(1+\sqrt{y)})/(sqrt(y))	\int\:\frac{\sqrt{1+\sqrt{y}}}{\sqrt{y}}dy
integral of (x-1)/((x^2+4x+5)(x+1))	\int\:\frac{x-1}{(x^{2}+4x+5)(x+1)}dx
(dy)/(dx)+x^2y=10x^2	\frac{dy}{dx}+x^{2}y=10x^{2}
y^{''}-3y^'+2y=4cos(4t)	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=4\cos(4t)
integral from 0 to 0.6 of 250x	\int\:_{0}^{0.6}250xdx

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