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Popular Calculus Problems

(\partial)/(\partial x)((e^x-x)sin(y))	\frac{\partial\:}{\partial\:x}((e^{x}-x)\sin(y))
xy^2(dy)/(dx)=y^3-x^3,y(1)=2	xy^{2}\frac{dy}{dx}=y^{3}-x^{3},y(1)=2
limit as x approaches 1 of x(x+1)	\lim\:_{x\to\:1}(x(x+1))
derivative of x/2 sqrt(x^2-1)	\frac{d}{dx}(\frac{x}{2}\sqrt{x^{2}-1})
derivative of sqrt(x^4-3x^2+4)	\frac{d}{dx}(\sqrt{x^{4}-3x^{2}+4})
derivative of (6x/(3-cot(x)))	\frac{d}{dx}(\frac{6x}{3-\cot(x)})
limit as x approaches 0 of x^3-1	\lim\:_{x\to\:0}(x^{3}-1)
derivative of 1/(3\sqrt[3]{x^2})	\frac{d}{dx}(\frac{1}{3\sqrt[3]{x^{2}}})
integral from 1 to 4 of-9sqrt(x)ln(x)	\int\:_{1}^{4}-9\sqrt{x}\ln(x)dx
limit as x approaches 0 of (2e^{-x}-x^2+2x-2)/(4x^3)	\lim\:_{x\to\:0}(\frac{2e^{-x}-x^{2}+2x-2}{4x^{3}})
y^'+xy=xy^3	y^{\prime\:}+x\cdot\:y=x\cdot\:y^{3}
sum from n=0 to infinity of 5(-4/3)^n	\sum\:_{n=0}^{\infty\:}5(-\frac{4}{3})^{n}
integral of (x^3-1/(x^2)-x^{2/3})	\int\:(x^{3}-\frac{1}{x^{2}}-x^{\frac{2}{3}})dx
integral of 36-(0.6x^2+2x+11)	\int\:36-(0.6x^{2}+2x+11)dx
integral from 0 to pi/2 of 1-4sin^2(x)	\int\:_{0}^{\frac{π}{2}}1-4\sin^{2}(x)dx
derivative of 2x^{-3/4}	derivative\:2x^{-\frac{3}{4}}
(dy)/(dx)=(1+e^{x^2})(5+x)	\frac{dy}{dx}=(1+e^{x^{2}})(5+x)
derivative of 4/(cos(x))+1/(tan(x))	derivative\:\frac{4}{\cos(x)}+\frac{1}{\tan(x)}
derivative of xe^{(-x^2})	\frac{d}{dx}(xe^{(-x^{2})})
derivative of ((4x^2+8x+2))/(sqrt(x))	derivative\:\frac{(4x^{2}+8x+2)}{\sqrt{x}}
y^'+175x=0,y(2)=0	y^{\prime\:}+175x=0,y(2)=0
(dy)/(dt)=4y+y^3,y(0)=1	\frac{dy}{dt}=4y+y^{3},y(0)=1
derivative of ln(\sqrt[8]{(x-3/(x+3)}))	\frac{d}{dx}(\ln(\sqrt[8]{\frac{x-3}{x+3}}))
laplacetransform te^{-10t}	laplacetransform\:te^{-10t}
integral of 1/(25e^{-2x)+e^{2x}}	\int\:\frac{1}{25e^{-2x}+e^{2x}}dx
area y^2-2x=9,x-y=3	area\:y^{2}-2x=9,x-y=3
integral of e^{xy^2}	\int\:e^{xy^{2}}dx
derivative of y=(x-5)^2+8	derivative\:y=(x-5)^{2}+8
integral of cos^3(3x)sin^4(3x)	\int\:\cos^{3}(3x)\sin^{4}(3x)dx
(\partial)/(\partial x)(x^3-3x+y-e^y)	\frac{\partial\:}{\partial\:x}(x^{3}-3x+y-e^{y})
(d^4)/(dx^4)(8sqrt(x))	\frac{d^{4}}{dx^{4}}(8\sqrt{x})
(\partial)/(\partial x)((3x-2y)/(5x+y))	\frac{\partial\:}{\partial\:x}(\frac{3x-2y}{5x+y})
derivative of-sin(x-cos(x))	\frac{d}{dx}(-\sin(x)-\cos(x))
derivative of-2x^2y	\frac{d}{dx}(-2x^{2}y)
y^'=y(xy^4+1)	y^{\prime\:}=y(xy^{4}+1)
integral of (x+1)/(sqrt(9-x^2))	\int\:\frac{x+1}{\sqrt{9-x^{2}}}dx
integral of 7sin(ln(x))	\int\:7\sin(\ln(x))dx
limit as x approaches 0 of 1/(sqrt(1+x))	\lim\:_{x\to\:0}(\frac{1}{\sqrt{1+x}})
integral of sin^6(x)	\int\:\sin^{6}(x)dx
limit as x approaches 0 of 1/(4x^2)	\lim\:_{x\to\:0}(\frac{1}{4x^{2}})
derivative of f(x)=1.8sin(x)-x	derivative\:f(x)=1.8\sin(x)-x
integral of (15)/((x-1)(x^2+4))	\int\:\frac{15}{(x-1)(x^{2}+4)}dx
f(x)=e^{5x}	f(x)=e^{5x}
(dy)/(dx)=(40)/(x^{-5)}	\frac{dy}{dx}=\frac{40}{x^{-5}}
sum from k=5 to infinity of 1/((k-2)^4)	\sum\:_{k=5}^{\infty\:}\frac{1}{(k-2)^{4}}
derivative of-(2e^{2/x}/(x^2))	\frac{d}{dx}(-\frac{2e^{\frac{2}{x}}}{x^{2}})
derivative of f(x)=2tan(sqrt(x))	derivative\:f(x)=2\tan(\sqrt{x})
integral of-(3sin(-x))/(cos(-x))	\int\:-\frac{3\sin(-x)}{\cos(-x)}dx
integral from-1 to 1 of pi(8-8x^2)^2	\int\:_{-1}^{1}π(8-8x^{2})^{2}dx
derivative of f(x)=sqrt(x)-(x+1)^4	derivative\:f(x)=\sqrt{x}-(x+1)^{4}
y^'=x-7	y^{\prime\:}=x-7
expand e^x(4-x)	expand\:e^{x}(4-x)
integral of (9r^2)/(sqrt(1-r^3))	\int\:\frac{9r^{2}}{\sqrt{1-r^{3}}}dr
sum from n=1 to infinity of n^3e^{-n^2}	\sum\:_{n=1}^{\infty\:}n^{3}e^{-n^{2}}
limit as x approaches-1 of (x+1)/(x^2+1)	\lim\:_{x\to\:-1}(\frac{x+1}{x^{2}+1})
integral of 1/3 e^x	\int\:\frac{1}{3}e^{x}dx
taylor ln(x),2	taylor\:\ln(x),2
derivative of y=3x^{3/8}	derivative\:y=3x^{\frac{3}{8}}
(dy)/(dx)=(1+y)(1-2x)	\frac{dy}{dx}=(1+y)(1-2x)
integral of (9x)/((x+3)^2)	\int\:\frac{9x}{(x+3)^{2}}dx
integral of (2/(x^5))	\int\:(\frac{2}{x^{5}})dx
integral of (4x-1)/(x^2-25)	\int\:\frac{4x-1}{x^{2}-25}dx
derivative of 5x^4-x^6	derivative\:5x^{4}-x^{6}
integral of xcsc(6x^2)	\int\:x\csc(6x^{2})dx
(dy)/(dt)=(te^t)/(ysqrt(5+y^2))	\frac{dy}{dt}=\frac{te^{t}}{y\sqrt{5+y^{2}}}
derivative of (sin(x)/((1+cos(x))^2))	\frac{d}{dx}(\frac{\sin(x)}{(1+\cos(x))^{2}})
derivative of e^{x,x}	\frac{d}{dx}(e^{x,x})
inverse oflaplace ((s+1))/((s^2+s+10))	inverselaplace\:\frac{(s+1)}{(s^{2}+s+10)}
integral from 4 to 8 of 1-4/x	\int\:_{4}^{8}1-\frac{4}{x}dx
derivative of f(x)=sqrt(5x+4)	derivative\:f(x)=\sqrt{5x+4}
sum from n=1 to infinity of 5^n	\sum\:_{n=1}^{\infty\:}5^{n}
(\partial)/(\partial x)(y+sqrt(x))	\frac{\partial\:}{\partial\:x}(y+\sqrt{x})
limit as x approaches infinity of (1-0.8^{x+1})/(1-0.8)	\lim\:_{x\to\:\infty\:}(\frac{1-0.8^{x+1}}{1-0.8})
inverse oflaplace 3/((s-3))	inverselaplace\:\frac{3}{(s-3)}
(\partial)/(\partial y)((x+2y^3)^{1/3})	\frac{\partial\:}{\partial\:y}((x+2y^{3})^{\frac{1}{3}})
integral from 0 to ln(3) of xe^x	\int\:_{0}^{\ln(3)}xe^{x}dx
derivative of f(x)=-2xe^{-x^2}	derivative\:f(x)=-2xe^{-x^{2}}
integral of 1/((y-1)^2)	\int\:\frac{1}{(y-1)^{2}}dy
limit as z approaches 2pii of e^z-e^{-z}	\lim\:_{z\to\:2πi}(e^{z}-e^{-z})
integral from 4 to 6 of 1/(sqrt(t^2-9))	\int\:_{4}^{6}\frac{1}{\sqrt{t^{2}-9}}dt
derivative of 1/(1+y^2+cos(x)-2xy)	\frac{d}{dx}(\frac{1}{1+y^{2}}+\cos(x)-2xy)
derivative of 4e^{x-3}	derivative\:4e^{x-3}
d/(d{y)}(sqrt({x)^2+{y}^2+{z}^2})	\frac{d}{d{y}}(\sqrt{{x}^{2}+{y}^{2}+{z}^{2}})
x*(dy)/(dx)+y=4x+1	x\cdot\:\frac{dy}{dx}+y=4x+1
(\partial)/(\partial x)(yarctan(x/y))	\frac{\partial\:}{\partial\:x}(y\arctan(\frac{x}{y}))
derivative of (x^2/(2^x))	\frac{d}{dx}(\frac{x^{2}}{2^{x}})
integral of 1/(x^2)-1	\int\:\frac{1}{x^{2}}-1dx
derivative of (2x^2-4x+4)e^x	derivative\:(2x^{2}-4x+4)e^{x}
taylor cos(x),1	taylor\:\cos(x),1
derivative of 4(x+4)^{3/2}	derivative\:4(x+4)^{\frac{3}{2}}
(dy)/(dx)+((1-y^2)/(1-y^2))^{1/2}=0	\frac{dy}{dx}+(\frac{1-y^{2}}{1-y^{2}})^{\frac{1}{2}}=0
(\partial)/(\partial z)(e^xcos(y)+yz)	\frac{\partial\:}{\partial\:z}(e^{x}\cos(y)+yz)
sum from n=1 to infinity of 2^{-4n}	\sum\:_{n=1}^{\infty\:}2^{-4n}
integral of sin(2pit)	\int\:\sin(2πt)dt
integral of 1/(sqrt(y)+y)	\int\:\frac{1}{\sqrt{y}+y}dy
integral of (x^3)/(x^2+30x+225)	\int\:\frac{x^{3}}{x^{2}+30x+225}dx
limit as t approaches 2 of (2t)/(4-t^2)	\lim\:_{t\to\:2}(\frac{2t}{4-t^{2}})
(dy)/(dx)=-3+2/1 (dy)/(dx)	\frac{dy}{dx}=-3+\frac{2}{1}\frac{dy}{dx}
derivative of f(x)=sqrt(15x)ln(4x)	derivative\:f(x)=\sqrt{15x}\ln(4x)
derivative of (7-xe^x/(x+e^x))	\frac{d}{dx}(\frac{7-xe^{x}}{x+e^{x}})

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