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Popular Calculus Problems

derivative of (2t^2+1)/t	derivative\:\frac{2t^{2}+1}{t}
derivative of xe^{-sqrt(x)}	\frac{d}{dx}(xe^{-\sqrt{x}})
taylor f(x)=cos(4x)	taylor\:f(x)=\cos(4x)
tangent of f(x)=2sqrt(x),\at x=4	tangent\:f(x)=2\sqrt{x},\at\:x=4
y^'=(3x^2+2x-4)/(2y-4),y(2)=0	y^{\prime\:}=\frac{3x^{2}+2x-4}{2y-4},y(2)=0
inverse oflaplace (2s)/((s^2+1)^2(s+1))	inverselaplace\:\frac{2s}{(s^{2}+1)^{2}(s+1)}
derivative of (xcos(x-sin(x))/(x^2))	\frac{d}{dx}(\frac{x\cos(x)-\sin(x)}{x^{2}})
limit as x approaches 3 of 10(x+3)	\lim\:_{x\to\:3}(10(x+3))
derivative of f(x)=6x^2-5x	derivative\:f(x)=6x^{2}-5x
sum from n=0 to infinity of 1/(n^{1/n)}	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{\frac{1}{n}}}
derivative of 9arctan(x+sqrt(1+x^2))	derivative\:9\arctan(x+\sqrt{1+x^{2}})
limit as x approaches 0 of 4-sqrt(x)	\lim\:_{x\to\:0}(4-\sqrt{x})
derivative of 2x^2sin(x)tan(x)	derivative\:2x^{2}\sin(x)\tan(x)
derivative of sqrt(cos(-10x))	derivative\:\sqrt{\cos(-10x)}
integral of x*tan(x)	\int\:x\cdot\:\tan(x)dx
(\partial)/(\partial x)(x/(1+x))	\frac{\partial\:}{\partial\:x}(\frac{x}{1+x})
tangent of 3(x)^2+8(x)+12	tangent\:3(x)^{2}+8(x)+12
limit as x approaches 2 of x/(x^2+1)	\lim\:_{x\to\:2}(\frac{x}{x^{2}+1})
y^{''}+4y^'-2y=2x^2-3x+6	y^{\prime\:\prime\:}+4y^{\prime\:}-2y=2x^{2}-3x+6
integral of (-3)/((2x)^2)	\int\:\frac{-3}{(2x)^{2}}dx
limit as x approaches 2 of 3x+2	\lim\:_{x\to\:2}(3x+2)
tangent of y=6x-x^2	tangent\:y=6x-x^{2}
derivative of (2e^x+x^2ln(x))	\frac{d}{dx}((2e^{x}+x^{2})\ln(x))
limit as x approaches 1 of x	\lim\:_{x\to\:1}(x)
inverse oflaplace 1/(s^2)-1/s+1/((s-2))	inverselaplace\:\frac{1}{s^{2}}-\frac{1}{s}+\frac{1}{(s-2)}
integral of (x^2+2x)/(x^2+2x+1)	\int\:\frac{x^{2}+2x}{x^{2}+2x+1}dx
derivative of x-3/x	\frac{d}{dx}(x-\frac{3}{x})
derivative of ln(x+sqrt(x^2-4))	\frac{d}{dx}(\ln(x+\sqrt{x^{2}-4}))
y^{''}-9y^'+18y=0	y^{\prime\:\prime\:}-9y^{\prime\:}+18y=0
derivative of x/(y^{13)}+Be^y	derivative\:\frac{x}{y^{13}}+Be^{y}
integral of (csc^4(θ))	\int\:(\csc^{4}(θ))dθ
derivative of (2x^3-4x^2(3x^5+x^2))	\frac{d}{dx}((2x^{3}-4x^{2})(3x^{5}+x^{2}))
integral of 2/(x^2+3x-4)	\int\:\frac{2}{x^{2}+3x-4}dx
integral from 0 to pi of cos(x/2)	\int\:_{0}^{π}\cos(\frac{x}{2})dx
limit as x approaches 1-of (\|-1\|)/(-1)	\lim\:_{x\to\:1-}(\frac{\left\|-1\right\|}{-1})
(\partial)/(\partial x)(x/(x^2+25))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+25})
integral of cos(sqrt(10x))	\int\:\cos(\sqrt{10x})dx
(\partial)/(\partial x)(xe^{2x+3y})	\frac{\partial\:}{\partial\:x}(xe^{2x+3y})
integral of e^{2x}cos(9x)	\int\:e^{2x}\cos(9x)dx
implicit (dy)/(dx),y= 2/x	implicit\:\frac{dy}{dx},y=\frac{2}{x}
integral of e^{-4x^2}	\int\:e^{-4x^{2}}dx
sum from n=1 to infinity of (cos(0.3))^n	\sum\:_{n=1}^{\infty\:}(\cos(0.3))^{n}
integral of (csc(x))/(csc(x)-sin(x))	\int\:\frac{\csc(x)}{\csc(x)-\sin(x)}dx
(dy)/(dt)+y=te^t	\frac{dy}{dt}+y=te^{t}
integral from-1 to 1 of \sqrt[3]{x}	\int\:_{-1}^{1}\sqrt[3]{x}dx
tangent of f(x)= 1/(2sqrt(x)),\at x=36	tangent\:f(x)=\frac{1}{2\sqrt{x}},\at\:x=36
derivative of f(x)=(tan(9x))/(1+sin(9x))	derivative\:f(x)=\frac{\tan(9x)}{1+\sin(9x)}
(2x+3y-1)dx-4(x+1)dy=0	(2x+3y-1)dx-4(x+1)dy=0
inverse oflaplace (e^{-2s})/(s(s-2))	inverselaplace\:\frac{e^{-2s}}{s(s-2)}
derivative of-2e^{5y}x-2sin(2x)	\frac{d}{dx}(-2e^{5y}x-2\sin(2x))
integral from-2 to 2 of (4-x^2)	\int\:_{-2}^{2}(4-x^{2})dx
taylor (1-x^2)^{1/2}	taylor\:(1-x^{2})^{\frac{1}{2}}
derivative of 6x^{1/2}	derivative\:6x^{\frac{1}{2}}
integral from 0 to 6 of (1497.6)(x)	\int\:_{0}^{6}(1497.6)(x)dx
sum from n=1 to infinity of 7/(4^{n-1)}	\sum\:_{n=1}^{\infty\:}\frac{7}{4^{n-1}}
integral of sqrt(x)-2	\int\:\sqrt{x}-2dx
(dy)/(dx)=y(4x^2+6)	\frac{dy}{dx}=y(4x^{2}+6)
y^{''}-6y^'+3y=0,y(0)=0,y^'(0)=5	y^{\prime\:\prime\:}-6y^{\prime\:}+3y=0,y(0)=0,y^{\prime\:}(0)=5
y^'=((3x^2-e^x))/((2y-5))	y^{\prime\:}=\frac{(3x^{2}-e^{x})}{(2y-5)}
limit as h approaches 0 of ((3+h)^2-9)/h	\lim\:_{h\to\:0}(\frac{(3+h)^{2}-9}{h})
((dy)/(dt))=2(y^2-y)t	(\frac{dy}{dt})=2(y^{2}-y)t
derivative of f(x)= 3/(sqrt(t))	derivative\:f(x)=\frac{3}{\sqrt{t}}
derivative of 2ln(x-x)	\frac{d}{dx}(2\ln(x)-x)
derivative of sin^2(sqrt(x))	\frac{d}{dx}(\sin^{2}(\sqrt{x}))
integral of (sqrt(x))/(\sqrt[3]{x)1}	\int\:\frac{\sqrt{x}}{\sqrt[3]{x}1}dx
y^{''}-4y^'+3y=e^{-x}	y^{\prime\:\prime\:}-4y^{\prime\:}+3y=e^{-x}
derivative of (5x+1)^2	derivative\:(5x+1)^{2}
tangent of f(x)=-3cos(x),\at x=-pi/4	tangent\:f(x)=-3\cos(x),\at\:x=-\frac{π}{4}
derivative of (7x+5^2)	\frac{d}{dx}((7x+5)^{2})
integral of x^3sqrt(x^2+27)	\int\:x^{3}\sqrt{x^{2}+27}dx
tangent of ((a+h)^4)/h	tangent\:\frac{(a+h)^{4}}{h}
derivative of (x^4-7x^2)	\frac{d}{dx}((x^{4}-7x)^{2})
y^'=y(xy^3-1)	y^{\prime\:}=y(xy^{3}-1)
derivative of f(x)=2^{80}	derivative\:f(x)=2^{80}
limit as x approaches 1 of 1+1/(x-1)	\lim\:_{x\to\:1}(1+\frac{1}{x-1})
integral of 2cos(2x)	\int\:2\cos(2x)dx
integral of (4x)/(sqrt(50-x^2))	\int\:\frac{4x}{\sqrt{50-x^{2}}}dx
taylor arctan(x^2)	taylor\:\arctan(x^{2})
(dy)/(dx)-(3x^2)/(2y)=0	\frac{dy}{dx}-\frac{3x^{2}}{2y}=0
derivative of arctan(2x^4)	\frac{d}{dx}(\arctan(2x^{4}))
integral of (x^2+3)^42x	\int\:(x^{2}+3)^{4}2xdx
integral of e^{-ax^2}	\int\:e^{-ax^{2}}dx
derivative of y=2\sqrt[3]{x}	derivative\:y=2\sqrt[3]{x}
tangent of y=(1+4x)^{11},(0,1)	tangent\:y=(1+4x)^{11},(0,1)
tangent of f(x)=(sqrt(x))/(x+6),\at x=4	tangent\:f(x)=\frac{\sqrt{x}}{x+6},\at\:x=4
derivative of e^{z/(z-6)}	derivative\:e^{\frac{z}{z-6}}
integral of (16s-4)/(3-2s+4s^2)	\int\:\frac{16s-4}{3-2s+4s^{2}}ds
derivative of y=tan(e^{3t})+e^{tan(3t)}	derivative\:y=\tan(e^{3t})+e^{\tan(3t)}
derivative of f(x)=e^r+r^e	derivative\:f(x)=e^{r}+r^{e}
integral of (3x)/(x^2)	\int\:\frac{3x}{x^{2}}dx
f^'(x)=3sec(x)	f^{\prime\:}(x)=3\sec(x)
integral from-1 to 4 of x/(sqrt(5+x))	\int\:_{-1}^{4}\frac{x}{\sqrt{5+x}}dx
limit as x approaches 3-of (\|x-3\|)/(x-3)	\lim\:_{x\to\:3-}(\frac{\left\|x-3\right\|}{x-3})
derivative of arcsin(sqrt(1-x))	\frac{d}{dx}(\arcsin(\sqrt{1-x}))
(dy)/(dt)=100-y,y(0)=15	\frac{dy}{dt}=100-y,y(0)=15
derivative of (2x-1)^2(x^3+1)^2	derivative\:(2x-1)^{2}(x^{3}+1)^{2}
derivative of y=cos((pit)/4-pi/3)	derivative\:y=\cos(\frac{πt}{4}-\frac{π}{3})
integral of 2/(x^5)	\int\:\frac{2}{x^{5}}dx
integral of cot(u)	\int\:\cot(u)du
y^'=2x(x-2)	y^{\prime\:}=2x(x-2)

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