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Popular Calculus Problems

2xy+x^2((dy)/(dx))=y^2	2xy+x^{2}(\frac{dy}{dx})=y^{2}
limit as x approaches 4 of sqrt(4x)+2	\lim\:_{x\to\:4}(\sqrt{4x}+2)
derivative of y=x^2+2x-3	derivative\:y=x^{2}+2x-3
derivative of 6/(sqrt(x))	derivative\:\frac{6}{\sqrt{x}}
tangent of y=e^s(s^3+5),(0,5)	tangent\:y=e^{s}(s^{3}+5),(0,5)
integral of (e^{6x})/(e^{2x)}	\int\:\frac{e^{6x}}{e^{2x}}dx
(\partial)/(\partial x)(sqrt(2x+y^{10)})	\frac{\partial\:}{\partial\:x}(\sqrt{2x+y^{10}})
integral of (pi^2-1)	\int\:(π^{2}-1)dx
integral of 4xln(6x)	\int\:4x\ln(6x)dx
100y^{''}-20y^'+y=0	100y^{\prime\:\prime\:}-20y^{\prime\:}+y=0
(x^2y+3y)y^'=2xy^2+8x	(x^{2}y+3y)y^{\prime\:}=2xy^{2}+8x
(dy)/(dx)=e^{-3y}	\frac{dy}{dx}=e^{-3y}
(dx)/(dt)=t^3(1-x),x(0)=3	\frac{dx}{dt}=t^{3}(1-x),x(0)=3
derivative of 3x^{k-2}+2kx^{k-1}+4x^k	\frac{d}{dx}(3x^{k-2}+2kx^{k-1}+4x^{k})
integral of x/((x-2)^3)	\int\:\frac{x}{(x-2)^{3}}dx
derivative of 1/4 e^x+3/4 e^{-x}	\frac{d}{dx}(\frac{1}{4}e^{x}+\frac{3}{4}e^{-x})
derivative of (1+x^2/x)	\frac{d}{dx}(\frac{1+x^{2}}{x})
limit as x approaches 4 of 6/x	\lim\:_{x\to\:4}(\frac{6}{x})
integral of xy^2	\int\:xy^{2}dx
simplify (x^2+2x)/(4x)	simplify\:\frac{x^{2}+2x}{4x}
(dy)/(dx)=-y+1	\frac{dy}{dx}=-y+1
integral of (4x-3)/(sqrt(x))	\int\:\frac{4x-3}{\sqrt{x}}dx
derivative of y=ln(5+2x+x^3)	derivative\:y=\ln(5+2x+x^{3})
integral of 1/(cos^2(ay))	\int\:\frac{1}{\cos^{2}(ay)}dy
(\partial)/(\partial x)(8x^2+y^2-9y)	\frac{\partial\:}{\partial\:x}(8x^{2}+y^{2}-9y)
tangent of f(x)=x^2+3x+1,\at x=4	tangent\:f(x)=x^{2}+3x+1,\at\:x=4
limit as x approaches 0 of ln(0)	\lim\:_{x\to\:0}(\ln(0))
integral of x^3(3+x^4)^5	\int\:x^{3}(3+x^{4})^{5}dx
(\partial)/(\partial x)(2x^2y+3)	\frac{\partial\:}{\partial\:x}(2x^{2}y+3)
(dr)/(dθ)r=(4+sec(θ))sin(θ)	\frac{dr}{dθ}r=(4+\sec(θ))\sin(θ)
derivative of f(x)=sqrt((x^2*5^x)^9)	derivative\:f(x)=\sqrt{(x^{2}\cdot\:5^{x})^{9}}
integral of 12x(3x^2-1)^3	\int\:12x(3x^{2}-1)^{3}dx
derivative of ce^{-2x}	\frac{d}{dx}(ce^{-2x})
integral from 1 to 2 of x^2-1	\int\:_{1}^{2}x^{2}-1dx
y^'=((1-2x))/y	y^{\prime\:}=\frac{(1-2x)}{y}
expand (x+5)e^{2x}+7	expand\:(x+5)e^{2x}+7
(dy)/(dt)=5*(y-t^2)	\frac{dy}{dt}=5\cdot\:(y-t^{2})
(\partial)/(\partial x)(1/((1-x)^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{(1-x)^{2}})
derivative of sin(t/2)	derivative\:\sin(\frac{t}{2})
derivative of xinx	\frac{d}{dx}(xinx)
integral of 1/(3+2x)	\int\:\frac{1}{3+2x}dx
integral of z^3	\int\:z^{3}dz
tangent of y= 1/(x^4),(3, 1/81)	tangent\:y=\frac{1}{x^{4}},(3,\frac{1}{81})
integral of 1/(sin^2(x))	\int\:\frac{1}{\sin^{2}(x)}dx
limit as x approaches 2+of (x+1)/(x-2)	\lim\:_{x\to\:2+}(\frac{x+1}{x-2})
integral from 0 to pi of 5sin^2(tco)s^4t	\int\:_{0}^{π}5\sin^{2}(tco)s^{4}tdt
tangent of f(x)=(ln(x))^4,\at x=2	tangent\:f(x)=(\ln(x))^{4},\at\:x=2
derivative of y=(x^3)/(5-x^2)	derivative\:y=\frac{x^{3}}{5-x^{2}}
(\partial)/(\partial x)(ln(x^2+y^4))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+y^{4}))
area y=2x^2+5x+6,(-2,0)	area\:y=2x^{2}+5x+6,(-2,0)
derivative of 1/2 x^2-1/4 x+1/3	\frac{d}{dx}(\frac{1}{2}x^{2}-\frac{1}{4}x+\frac{1}{3})
integral of 4(cos(x))/(sin^2(x))	\int\:4\frac{\cos(x)}{\sin^{2}(x)}dx
derivative of 2x^2-7x+5	derivative\:2x^{2}-7x+5
(\partial)/(\partial x)(Ce^{2x})	\frac{\partial\:}{\partial\:x}(Ce^{2x})
derivative of x/(sqrt(x)+1)	derivative\:\frac{x}{\sqrt{x}+1}
derivative of x^2+5-3x^{-2}	\frac{d}{dx}(x^{2}+5-3x^{-2})
integral of x^5cos(y^4)	\int\:x^{5}\cos(y^{4})dx
(\partial)/(\partial u)(vcos(u))	\frac{\partial\:}{\partial\:u}(v\cos(u))
(d^2)/(dx^2)(sin^2(x))	\frac{d^{2}}{dx^{2}}(\sin^{2}(x))
derivative of 4/(x^4-5\sqrt[3]{x})	\frac{d}{dx}(\frac{4}{x^{4}}-5\sqrt[3]{x})
integral of 5/(x^2+4)	\int\:\frac{5}{x^{2}+4}dx
integral of (2x^3-2x^2+1)/(x^2-x)	\int\:\frac{2x^{3}-2x^{2}+1}{x^{2}-x}dx
limit as x approaches infinity of (3^{x-3})/(2^{n+3)}	\lim\:_{x\to\:\infty\:}(\frac{3^{x-3}}{2^{n+3}})
limit as x approaches 2-of x+4	\lim\:_{x\to\:2-}(x+4)
3y(x^2-1)dx+(x^3+8y-3x)dy=0	3y(x^{2}-1)dx+(x^{3}+8y-3x)dy=0
slope of y=x^2-5	slope\:y=x^{2}-5
derivative of f(x)= 1/2 x-1/3	derivative\:f(x)=\frac{1}{2}x-\frac{1}{3}
derivative of (470t)/((t^2+6)^3)	derivative\:\frac{470t}{(t^{2}+6)^{3}}
y^{''}-6y^'+8y=-4e^{3t}	y^{\prime\:\prime\:}-6y^{\prime\:}+8y=-4e^{3t}
(\partial ^2)/(\partial y^2)(2cos(xy^2))	\frac{\partial\:^{2}}{\partial\:y^{2}}(2\cos(xy^{2}))
tangent of f(x)=4x^2-5x,\at x=-3	tangent\:f(x)=4x^{2}-5x,\at\:x=-3
(\partial)/(\partial x)(x^2ln(y-1))	\frac{\partial\:}{\partial\:x}(x^{2}\ln(y-1))
integral from 1 to 2 of x(x-1)^4	\int\:_{1}^{2}x(x-1)^{4}dx
integral of ln(t)*t^2	\int\:\ln(t)\cdot\:t^{2}dt
limit as x approaches+(-infinity)+of x^5	\lim\:_{x\to\:+(-\infty\:)+}(x^{5})
(dy)/(dx)=(5x)/(2y)	\frac{dy}{dx}=\frac{5x}{2y}
area y=x^{-3},1<= x<= 6	area\:y=x^{-3},1\le\:x\le\:6
integral from-2 to 2 of x^2-2	\int\:_{-2}^{2}x^{2}-2dx
integral of ln(3-x)	\int\:\ln(3-x)dx
integral from 1 to 2 of (sqrt(x-1))/(2x)	\int\:_{1}^{2}\frac{\sqrt{x-1}}{2x}dx
(\partial}{\partial y}(sin(\frac{5x)/y))	\frac{\partial\:}{\partial\:y}(\sin(\frac{5x}{y}))
area y= 4/x ,y=x,y=4	area\:y=\frac{4}{x},y=x,y=4
integral of 5x^2(x^3+1)^{10}	\int\:5x^{2}(x^{3}+1)^{10}dx
derivative of f(x)=(5x^3+4)(3x^7-5)	derivative\:f(x)=(5x^{3}+4)(3x^{7}-5)
integral of (x+4)/(x^2+7x-8)	\int\:\frac{x+4}{x^{2}+7x-8}dx
2y^{''}-3y^'+y=e^{-3x}	2y^{\prime\:\prime\:}-3y^{\prime\:}+y=e^{-3x}
integral of tan(bx)	\int\:\tan(bx)dx
integral of e^{-θ}cos(7θ)	\int\:e^{-θ}\cos(7θ)dθ
integral of-2/(x^6)	\int\:-\frac{2}{x^{6}}dx
integral of ((2x^3+x^2-3x)/x)	\int\:(\frac{2x^{3}+x^{2}-3x}{x})dx
derivative of \sqrt[4]{x^4-2}	\frac{d}{dx}(\sqrt[4]{x^{4}-2})
integral of (9/(sqrt(x))+9sqrt(x))	\int\:(\frac{9}{\sqrt{x}}+9\sqrt{x})dx
derivative of f(x)=9x+13xe^x	derivative\:f(x)=9x+13xe^{x}
(\partial)/(\partial z)(x^2e^{yz})	\frac{\partial\:}{\partial\:z}(x^{2}e^{yz})
limit as x approaches 0 of (x^3+5x)/x	\lim\:_{x\to\:0}(\frac{x^{3}+5x}{x})
integral from 0 to x of 1/(t^2-25)	\int\:_{0}^{x}\frac{1}{t^{2}-25}dt
y^'=y+3te^t,y(0)=4	y^{\prime\:}=y+3te^{t},y(0)=4
limit as x approaches 3 of sqrt(x-8)	\lim\:_{x\to\:3}(\sqrt{x-8})
integral of (s^3+3)^2(1-s^2)^3	\int\:(s^{3}+3)^{2}(1-s^{2})^{3}ds
y^{''}-16y=2e^{4x}	y^{\prime\:\prime\:}-16y=2e^{4x}

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