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Popular Calculus Problems

derivative of (ln(x)/(5ln(x)+4))	\frac{d}{dx}(\frac{\ln(x)}{5\ln(x)+4})
integral from 1 to 4 of sqrt(t)ln(t)	\int\:_{1}^{4}\sqrt{t}\ln(t)dt
slope of y=x+3y=x+1y=-x+1	slope\:y=x+3y=x+1y=-x+1
derivative of (3x+2/(x-1))	\frac{d}{dx}(\frac{3x+2}{x-1})
derivative of (e^x/(x+1))	\frac{d}{dx}(\frac{e^{x}}{x+1})
integral of (e^{x/2})/2	\int\:\frac{e^{\frac{x}{2}}}{2}dx
sum from n=0 to infinity of (-5/8)^n	\sum\:_{n=0}^{\infty\:}(-\frac{5}{8})^{n}
derivative of log_{e}(1/(csc(x)))	derivative\:\log_{e}(\frac{1}{\csc(x)})
taylor (1+x)^{1/x}	taylor\:(1+x)^{\frac{1}{x}}
y^{'''}+10y^{''}+25y^'=0	y^{\prime\:\prime\:\prime\:}+10y^{\prime\:\prime\:}+25y^{\prime\:}=0
(\partial)/(\partial x)(-2xy+x^3)	\frac{\partial\:}{\partial\:x}(-2xy+x^{3})
tangent of f(x)=2-3x^2,\at x=-2	tangent\:f(x)=2-3x^{2},\at\:x=-2
(dy)/(dx)=y^2-2y	\frac{dy}{dx}=y^{2}-2y
derivative of e^{2x}*sin(x^2+5)	\frac{d}{dx}(e^{2x}\cdot\:\sin(x^{2}+5))
tangent of 2x^3-x^2+3	tangent\:2x^{3}-x^{2}+3
d/(dy)(ln(sqrt(x^2+y^2)))	\frac{d}{dy}(\ln(\sqrt{x^{2}+y^{2}}))
(dy)/(dx)=(x+y+9)^2	\frac{dy}{dx}=(x+y+9)^{2}
integral from-2 to 3 of (25)/(x^4)	\int\:_{-2}^{3}\frac{25}{x^{4}}dx
derivative of 1/(2\sqrt[3]{x^2})	\frac{d}{dx}(\frac{1}{2\sqrt[3]{x^{2}}})
integral from 0 to infinity of sin(4x)	\int\:_{0}^{\infty\:}\sin(4x)dx
integral of (-9)/(sqrt(x^2+16))	\int\:\frac{-9}{\sqrt{x^{2}+16}}dx
(d^2)/(dx^2)((3x^2+6x)sin(x))	\frac{d^{2}}{dx^{2}}((3x^{2}+6x)\sin(x))
derivative of cos(2x-1tan(1-2x))	\frac{d}{dx}(\cos(2x-1)\tan(1-2x))
area e^x,xe^{x^2},[0,1]	area\:e^{x},xe^{x^{2}},[0,1]
derivative of f(x)= 1/((3-x)^2)	derivative\:f(x)=\frac{1}{(3-x)^{2}}
limit as x approaches 0-of \sqrt[3]{x}	\lim\:_{x\to\:0-}(\sqrt[3]{x})
derivative of 4t^{(-3)/8}	derivative\:4t^{\frac{-3}{8}}
derivative of pi/6	\frac{d}{dx}(\frac{π}{6})
y^{''}+2y^'-8y=6e-2x-e-x	y^{\prime\:\prime\:}+2y^{\prime\:}-8y=6e-2x-e-x
derivative of (ax/(b+c))	\frac{d}{dx}(\frac{ax}{b+c})
integral of (sin^4(cot(x)))/(sin^2(x))	\int\:\frac{\sin^{4}(\cot(x))}{\sin^{2}(x)}dx
(\partial)/(\partial y)(tan(x^3y^2))	\frac{\partial\:}{\partial\:y}(\tan(x^{3}y^{2}))
(\partial)/(\partial x)(cos(x^2-y))	\frac{\partial\:}{\partial\:x}(\cos(x^{2}-y))
integral of (2x)/(sqrt(x-1))	\int\:\frac{2x}{\sqrt{x-1}}dx
(\partial)/(\partial y)(3y)	\frac{\partial\:}{\partial\:y}(3y)
4y^{''}-4y^'+4y=0	4y^{\prime\:\prime\:}-4y^{\prime\:}+4y=0
(\partial)/(\partial x)(xy+xcos(x))	\frac{\partial\:}{\partial\:x}(xy+x\cos(x))
x^{''}+9x-27=0,x(0)=4,x^'(0)=6	x^{\prime\:\prime\:}+9x-27=0,x(0)=4,x^{\prime\:}(0)=6
integral of 1/(12y)	\int\:\frac{1}{12y}dy
(\partial)/(\partial y)((y-t)/(5y+2t))	\frac{\partial\:}{\partial\:y}(\frac{y-t}{5y+2t})
laplacetransform t-pi	laplacetransform\:t-π
integral of (x^2)/((x^2+1)^2)	\int\:\frac{x^{2}}{(x^{2}+1)^{2}}dx
derivative of ln(sqrt(x^2-4))	\frac{d}{dx}(\ln(\sqrt{x^{2}-4}))
d/(dt)(e^{5tsin(2t)})	\frac{d}{dt}(e^{5t\sin(2t)})
derivative of e^{ln(x})	\frac{d}{dx}(e^{\ln(x)})
derivative of sqrt((x^2-1)/(x^2+1))	derivative\:\sqrt{\frac{x^{2}-1}{x^{2}+1}}
sum from n=2 to infinity of ln(1/n)	\sum\:_{n=2}^{\infty\:}\ln(\frac{1}{n})
inverse oflaplace 1/(2x^2+x+1)	inverselaplace\:\frac{1}{2x^{2}+x+1}
(dN)/(dt)=5-N,N(2)=2	\frac{dN}{dt}=5-N,N(2)=2
integral of ((e^x-e^{-x})/2)	\int\:(\frac{e^{x}-e^{-x}}{2})dx
integral of (1/(e^x+e^{2x)})/(-e^{-3x)}	\int\:\frac{\frac{1}{e^{x}+e^{2x}}}{-e^{-3x}}dx
limit as x approaches 2-of (x-1)/(\|x-1\|)	\lim\:_{x\to\:2-}(\frac{x-1}{\left\|x-1\right\|})
derivative of 3x^3y^2	\frac{d}{dx}(3x^{3}y^{2})
(dy)/(dx)=(2x+sec^2(x))/(4y)	\frac{dy}{dx}=\frac{2x+\sec^{2}(x)}{4y}
(\partial)/(\partial y)(yln(x))	\frac{\partial\:}{\partial\:y}(y\ln(x))
derivative of 40x^4+180x^3+240x^2+100x	\frac{d}{dx}(40x^{4}+180x^{3}+240x^{2}+100x)
derivative of 1/3 (3-5x^3)	\frac{d}{dx}(\frac{1}{3}(3-5x)^{3})
integral from 0 to 2 of (16)/(21x^2)	\int\:_{0}^{2}\frac{16}{21x^{2}}dx
tangent of 9x^2,\at x=2	tangent\:9x^{2},\at\:x=2
integral of x/(x^2-x+6)	\int\:\frac{x}{x^{2}-x+6}dx
(\partial)/(\partial x)(a/(x^2))	\frac{\partial\:}{\partial\:x}(\frac{a}{x^{2}})
(\partial)/(\partial x)(ln(x^6y))	\frac{\partial\:}{\partial\:x}(\ln(x^{6}y))
(dy)/(dx)+y/x =8x^5y^2	\frac{dy}{dx}+\frac{y}{x}=8x^{5}y^{2}
integral from 0 to 6 of (8t)/((t-7)^2)	\int\:_{0}^{6}\frac{8t}{(t-7)^{2}}dt
(\partial)/(\partial x)((z(x+y))/(x+y+z))	\frac{\partial\:}{\partial\:x}(\frac{z(x+y)}{x+y+z})
x^'=-2x	x^{\prime\:}=-2x
limit as x approaches-10 of-(1/(x+10))	\lim\:_{x\to\:-10}(-(\frac{1}{x+10}))
integral from 0 to x of sqrt(x^2+x^4)	\int\:_{0}^{x}\sqrt{x^{2}+x^{4}}dx
derivative of ax^2e^{3x}	\frac{d}{dx}(ax^{2}e^{3x})
integral of 2cos(x)cos(2x)	\int\:2\cos(x)\cos(2x)dx
derivative of arctan(0)	\frac{d}{dx}(\arctan(0))
(\partial)/(\partial y)(x/(x+y))	\frac{\partial\:}{\partial\:y}(\frac{x}{x+y})
(\partial)/(\partial y)(-1/4 (y^2+x^2))	\frac{\partial\:}{\partial\:y}(-\frac{1}{4}(y^{2}+x^{2}))
limit as x approaches-5 of (x+3)/(x+5)	\lim\:_{x\to\:-5}(\frac{x+3}{x+5})
integral of 3cos^2(t)	\int\:3\cos^{2}(t)dt
(d^2y)/(dx^2)+9y=0	\frac{d^{2}y}{dx^{2}}+9y=0
derivative of 6x^3-tan(x)	derivative\:6x^{3}-\tan(x)
(\partial)/(\partial x)(xy(1-7x-4y))	\frac{\partial\:}{\partial\:x}(xy(1-7x-4y))
area 8cos(2x),8-8cos(2x),0, pi/2	area\:8\cos(2x),8-8\cos(2x),0,\frac{π}{2}
limit as x approaches 0+of x-1/(x^3)	\lim\:_{x\to\:0+}(x-\frac{1}{x^{3}})
(\partial)/(\partial x)(ln(1+x^2+e^y+z))	\frac{\partial\:}{\partial\:x}(\ln(1+x^{2}+e^{y}+z))
tangent of y=sec(x),(pi/6 ,(2sqrt(3))/3)	tangent\:y=\sec(x),(\frac{π}{6},\frac{2\sqrt{3}}{3})
2xy^'-8y=x^{-4}	2xy^{\prime\:}-8y=x^{-4}
derivative of-1/(2sqrt(1-x))	derivative\:-\frac{1}{2\sqrt{1-x}}
integral of sqrt(1+t^4)	\int\:\sqrt{1+t^{4}}dt
limit as t approaches 0 of e^{-6t}	\lim\:_{t\to\:0}(e^{-6t})
integral of (x^2-16)/(x(x+2)^3)	\int\:\frac{x^{2}-16}{x(x+2)^{3}}dx
(\partial)/(\partial x)(-sqrt(x^2+y^2))	\frac{\partial\:}{\partial\:x}(-\sqrt{x^{2}+y^{2}})
t^2y^{''}-2y=3t^2-1	t^{2}y^{\prime\:\prime\:}-2y=3t^{2}-1
limit as x approaches 0 of ((1))/x	\lim\:_{x\to\:0}(\frac{(1)}{x})
y^'=(1-y)(2-y)	y^{\prime\:}=(1-y)(2-y)
(ln(e))^'	(\ln(e))^{\prime\:}
derivative of e^{-(x-1^2})	\frac{d}{dx}(e^{-(x-1)^{2}})
(dy)/(dx)=(4cos^2(y)tan(x))	\frac{dy}{dx}=(4\cos^{2}(y)\tan(x))
derivative of (1/(y^2)-9/(y^4))(y+7y^3)	derivative\:(\frac{1}{y^{2}}-\frac{9}{y^{4}})(y+7y^{3})
integral of-8sin(x)	\int\:-8\sin(x)dx
integral of (x^2-x+8)/(x^3+2x)	\int\:\frac{x^{2}-x+8}{x^{3}+2x}dx
integral of (x+1)(sqrt(3x+2))	\int\:(x+1)(\sqrt{3x+2})dx
tangent of f(x)=x^3-12x	tangent\:f(x)=x^{3}-12x
integral of (3/5)cos(x)	\int\:(\frac{3}{5})\cos(x)dx

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