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Popular Calculus Problems

(dy)/(dx)=1+y^2	\frac{dy}{dx}=1+y^{2}
3x(dy)/(dx)-2y=(x^3)/(y^2)	3x\frac{dy}{dx}-2y=\frac{x^{3}}{y^{2}}
derivative of e^{-(x^2/2-(y^2)/2})	\frac{d}{dx}(e^{-\frac{x^{2}}{2}-\frac{y^{2}}{2}})
derivative of e^x	derivative\:e^{x}
(\partial)/(\partial x)((2x-2z)/(y+2z))	\frac{\partial\:}{\partial\:x}(\frac{2x-2z}{y+2z})
laplacetransform-5sin(3t)	laplacetransform\:-5\sin(3t)
(\partial)/(\partial y)((y^2)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{y^{2}}{x^{2}+y^{2}})
integral of-e^xx	\int\:-e^{x}xdx
integral of (36)/(1+36x^2)	\int\:\frac{36}{1+36x^{2}}dx
y^'=1-2y	y^{\prime\:}=1-2y
derivative of f(x)= x/(1-ln(x-4))	derivative\:f(x)=\frac{x}{1-\ln(x-4)}
tangent of f(x)=(1+3x)(5-4x),\at x=1	tangent\:f(x)=(1+3x)(5-4x),\at\:x=1
derivative of acos(ax)	\frac{d}{dx}(a\cos(ax))
integral of (x^3+4)/(x^2+4)	\int\:\frac{x^{3}+4}{x^{2}+4}dx
(\partial)/(\partial x)(cos(x-y)+(x+y))	\frac{\partial\:}{\partial\:x}(\cos(x-y)+(x+y))
area y=x,y=2xsqrt(25-x^2)	area\:y=x,y=2x\sqrt{25-x^{2}}
integral from-2 to 2 of-2x^2+8	\int\:_{-2}^{2}-2x^{2}+8dx
derivative of f(x)=(-2)/(x^2)	derivative\:f(x)=\frac{-2}{x^{2}}
derivative of 1/(x^2+18x+88)	derivative\:\frac{1}{x^{2}+18x+88}
derivative of y=sqrt(x)(x-4)	derivative\:y=\sqrt{x}(x-4)
integral of-1/2 cos(2x)(2x)	\int\:-\frac{1}{2}\cos(2x)(2x)dx
derivative of (x+3/(7x^2e^x))	\frac{d}{dx}(\frac{x+3}{7x^{2}e^{x}})
derivative of 16cos(x)	\frac{d}{dx}(16\cos(x))
integral of pi*x^2	\int\:π\cdot\:x^{2}dx
integral of 1/(sqrt(3x+2))	\int\:\frac{1}{\sqrt{3x+2}}dx
derivative of 9x^2sqrt(x)+2x^2	derivative\:9x^{2}\sqrt{x}+2x^{2}
laplacetransform e^{-2t}cos(5t)	laplacetransform\:e^{-2t}\cos(5t)
derivative of \sqrt[4]{5/4 x}	\frac{d}{dx}(\sqrt[4]{\frac{5}{4}x})
integral of 1/(x^2-2x+26)	\int\:\frac{1}{x^{2}-2x+26}dx
x^{''}-ax=0	x^{\prime\:\prime\:}-ax=0
limit as x approaches 0 of x^2cos(8/x)	\lim\:_{x\to\:0}(x^{2}\cos(\frac{8}{x}))
derivative of y=(3x-2)/x	derivative\:y=\frac{3x-2}{x}
derivative of (x^2-1/(x^3+x+1))	\frac{d}{dx}(\frac{x^{2}-1}{x^{3}+x+1})
(\partial)/(\partial t)(4sin(t))	\frac{\partial\:}{\partial\:t}(4\sin(t))
area y= 1/2 x,y= 1/25 x^2,y=1	area\:y=\frac{1}{2}x,y=\frac{1}{25}x^{2},y=1
limit as x approaches 5 of (2x)/(x-5)	\lim\:_{x\to\:5}(\frac{2x}{x-5})
limit as x approaches 9 of sqrt(f(x))	\lim\:_{x\to\:9}(\sqrt{f(x)})
derivative of sqrt(10)x+sqrt(7x)	\frac{d}{dx}(\sqrt{10}x+\sqrt{7x})
derivative of f(x)=(4x+1)^2	derivative\:f(x)=(4x+1)^{2}
derivative of 2x^4-5x^3+x^2	\frac{d}{dx}(2x^{4}-5x^{3}+x^{2})
integral from-1 to 2 of 3x^2+4x	\int\:_{-1}^{2}3x^{2}+4xdx
integral of-4x+12	\int\:-4x+12dx
y^'=y^2x^3	y^{\prime\:}=y^{2}x^{3}
area 3x^2+12,4x+4,[-3,3]	area\:3x^{2}+12,4x+4,[-3,3]
derivative of 1/(1+x+x^2+x^3)	derivative\:\frac{1}{1+x+x^{2}+x^{3}}
derivative of (18/((1+3x)^3))	\frac{d}{dx}(\frac{18}{(1+3x)^{3}})
inverse oflaplace (25s)/((s^2+9)(s+4))	inverselaplace\:\frac{25s}{(s^{2}+9)(s+4)}
derivative of sqrt(1+sin^2(x))	derivative\:\sqrt{1+\sin^{2}(x)}
y^'-2/t y=t^2	y^{\prime\:}-\frac{2}{t}y=t^{2}
derivative of-(8x/((4x^2+1)^2))	\frac{d}{dx}(-\frac{8x}{(4x^{2}+1)^{2}})
derivative of arcsin(coth(x))	\frac{d}{dx}(\arcsin(\coth(x)))
simplify ln(7x)	simplify\:\ln(7x)
derivative of (-3/(\sqrt[3]{x^2)})	\frac{d}{dx}(\frac{-3}{\sqrt[3]{x^{2}}})
area y=6-x^2,y=26-9x	area\:y=6-x^{2},y=26-9x
y^{'''}+y=0	y^{\prime\:\prime\:\prime\:}+y=0
limit as x approaches 9 of 4*a+x	\lim\:_{x\to\:9}(4\cdot\:a+x)
limit as x approaches 5-of (x^2)/(x^2+6)	\lim\:_{x\to\:5-}(\frac{x^{2}}{x^{2}+6})
integral of 9(x^3)/(x^7)	\int\:9\frac{x^{3}}{x^{7}}dx
derivative of cos(arcsin(2x))	\frac{d}{dx}(\cos(\arcsin(2x)))
area x^2-x-4,-x^2+3x+2	area\:x^{2}-x-4,-x^{2}+3x+2
integral of 12(y^4+4y^2+5)^2(y^3+2y)	\int\:12(y^{4}+4y^{2}+5)^{2}(y^{3}+2y)dy
(dy)/(dx)=sin^2(x-y+1)	\frac{dy}{dx}=\sin^{2}(x-y+1)
integral of e^{(x^2)/2}	\int\:e^{\frac{x^{2}}{2}}dx
d/(ds)(t/s)	\frac{d}{ds}(\frac{t}{s})
integral of (x^{5/6})	\int\:(x^{\frac{5}{6}})dx
integral of 30x^{3/2}	\int\:30x^{\frac{3}{2}}dx
y^'+5y=10	y^{\prime\:}+5y=10
integral of (2x^3-4x^2-15x+5)/(x^2-2x-8)	\int\:\frac{2x^{3}-4x^{2}-15x+5}{x^{2}-2x-8}dx
(\partial)/(\partial z)(sqrt(xyz))	\frac{\partial\:}{\partial\:z}(\sqrt{xyz})
derivative of cos(pi/4)	\frac{d}{dx}(\cos(\frac{π}{4}))
derivative of log_{10}(arcsin(cos(x)))	\frac{d}{dx}(\log_{10}(\arcsin(\cos(x))))
integral of (sin(2x))/(15+cos^2(x))	\int\:\frac{\sin(2x)}{15+\cos^{2}(x)}dx
integral of (10)/(x^2-1)	\int\:\frac{10}{x^{2}-1}dx
area y=x^{1/2},y=x-2,[0,4]	area\:y=x^{\frac{1}{2}},y=x-2,[0,4]
inverse oflaplace ((s+1))/((s^2+2s+2))	inverselaplace\:\frac{(s+1)}{(s^{2}+2s+2)}
laplacetransform cos^3(t)	laplacetransform\:\cos^{3}(t)
(dy)/(dx)=(6ye^{3x})/(2+e^{3x)}	\frac{dy}{dx}=\frac{6ye^{3x}}{2+e^{3x}}
integral from-infinity to-1 of e^{-28t}	\int\:_{-\infty\:}^{-1}e^{-28t}dt
derivative of x(x-1^2(x-2)^3)	\frac{d}{dx}(x(x-1)^{2}(x-2)^{3})
integral of pi^pi	\int\:π^{π}dx
derivative of y=x(3x+4)^5	derivative\:y=x(3x+4)^{5}
derivative of y= 1/((x+1)^2)	derivative\:y=\frac{1}{(x+1)^{2}}
(\partial)/(\partial x)((9xz)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{9xz}{x+y})
integral of (x^2-6x-17)/((x-1)^2(x^2+1))	\int\:\frac{x^{2}-6x-17}{(x-1)^{2}(x^{2}+1)}dx
integral from 0 to 3 of (9-x^2)	\int\:_{0}^{3}(9-x^{2})dx
(\partial)/(\partial x)(3sqrt(xy^2+9x))	\frac{\partial\:}{\partial\:x}(3\sqrt{xy^{2}+9x})
f(x)=x*sqrt(2x+2)	f(x)=x\cdot\:\sqrt{2x+2}
y^'=e^{(x+y)}	y^{\prime\:}=e^{(x+y)}
derivative of h(x)=(5-5x^3)^3+1/(5-5x^3)	derivative\:h(x)=(5-5x^{3})^{3}+\frac{1}{5-5x^{3}}
integral from 0 to pi of 6sin(x)	\int\:_{0}^{π}6\sin(x)dx
integral of sec(t)(9sec(t)+7tan(t))	\int\:\sec(t)(9\sec(t)+7\tan(t))dt
inverse oflaplace (10)/(s^2+2s+5)	inverselaplace\:\frac{10}{s^{2}+2s+5}
integral of 1/(sqrt(x^2-441))	\int\:\frac{1}{\sqrt{x^{2}-441}}dx
integral of-16sin(4x-pi/2)	\int\:-16\sin(4x-\frac{π}{2})dx
sum from n=1 to infinity of 1/n-1/(n+2)	\sum\:_{n=1}^{\infty\:}\frac{1}{n}-\frac{1}{n+2}
integral of (21xe^{2x})/((1+2x)^2)	\int\:\frac{21xe^{2x}}{(1+2x)^{2}}dx
y^'=3y,y(2)=4	y^{\prime\:}=3y,y(2)=4
derivative of 1+1/x+1/(x^2)	\frac{d}{dx}(1+\frac{1}{x}+\frac{1}{x^{2}})
integral of x^2+kx+1	\int\:x^{2}+kx+1dx
tangent of 12(x-1/x)^4,\at x=2	tangent\:12(x-\frac{1}{x})^{4},\at\:x=2

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