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Popular Calculus Problems

derivative of 2/(sqrt(x+3))	derivative\:\frac{2}{\sqrt{x+3}}
derivative of 18(4e^{x^2}x^3+6e^{x^2}x)	derivative\:18(4e^{x^{2}}x^{3}+6e^{x^{2}}x)
(\partial)/(\partial w)(usqrt(v-w))	\frac{\partial\:}{\partial\:w}(u\sqrt{v-w})
integral of e^{3ln(x)}	\int\:e^{3\ln(x)}dx
derivative of 12xe^{-x}	derivative\:12xe^{-x}
sum from n=1 to infinity of n/(2n+5)	\sum\:_{n=1}^{\infty\:}\frac{n}{2n+5}
inverse oflaplace 1-tan((xpi)/2)	inverselaplace\:1-\tan(\frac{xπ}{2})
derivative of 6x^3cot(x)	\frac{d}{dx}(6x^{3}\cot(x))
slope of (2.4)(6.11)	slope\:(2.4)(6.11)
(\partial)/(\partial y)(9e^xcos(yz))	\frac{\partial\:}{\partial\:y}(9e^{x}\cos(yz))
(f(x)e^{g(x)})\prime	(f(x)e^{g(x)})\prime
derivative of sqrt(x)-x	\frac{d}{dx}(\sqrt{x}-x)
(d^3)/(dx^3)(e^{2x})	\frac{d^{3}}{dx^{3}}(e^{2x})
limit as x approaches 0 of (1-x)/(x^2)	\lim\:_{x\to\:0}(\frac{1-x}{x^{2}})
y^{''}+4y=20	y^{\prime\:\prime\:}+4y=20
integral of 5x-sqrt(x)	\int\:5x-\sqrt{x}dx
(\partial)/(\partial x)(sqrt(4x^2+2y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{4x^{2}+2y^{2}})
xy^'+2y=-4e^x	xy^{\prime\:}+2y=-4e^{x}
derivative of-8sqrt(x)	\frac{d}{dx}(-8\sqrt{x})
limit as x approaches 0+of 0	\lim\:_{x\to\:0+}(0)
derivative of xsqrt(7-x^2)	derivative\:x\sqrt{7-x^{2}}
integral of (18x+2)	\int\:(18x+2)dx
integral from 0 to 2 of 2/(y^2+y-20)	\int\:_{0}^{2}\frac{2}{y^{2}+y-20}dy
derivative of f(x)=-8x^3	derivative\:f(x)=-8x^{3}
integral of (x^2+7x+1)/((x^2+1)^2)	\int\:\frac{x^{2}+7x+1}{(x^{2}+1)^{2}}dx
(\partial)/(\partial y)(2xy^4-3)	\frac{\partial\:}{\partial\:y}(2xy^{4}-3)
integral of (x+2)/(x^2+5x-6)	\int\:\frac{x+2}{x^{2}+5x-6}dx
integral from 0 to 1 of x^2x	\int\:_{0}^{1}x^{2}xdx
derivative of x/(x^2-7)	derivative\:\frac{x}{x^{2}-7}
integral of (x^4-x^2+1/(x^3)-1/(x^2))	\int\:(x^{4}-x^{2}+\frac{1}{x^{3}}-\frac{1}{x^{2}})dx
integral of 3+2xy	\int\:3+2xydx
derivative of y=-2x-4	derivative\:y=-2x-4
derivative of (Ax+B/(sqrt(4-x)))	\frac{d}{dx}(\frac{Ax+B}{\sqrt{4-x}})
sum from n=1 to infinity of 3/(n!)	\sum\:_{n=1}^{\infty\:}\frac{3}{n!}
(\partial)/(\partial x)(4xy^2)	\frac{\partial\:}{\partial\:x}(4xy^{2})
limit as x approaches 3 of sqrt(9-9)	\lim\:_{x\to\:3}(\sqrt{9-9})
(\partial)/(\partial x)((xy)/(x^2-y^2))	\frac{\partial\:}{\partial\:x}(\frac{xy}{x^{2}-y^{2}})
(\partial}{\partial x}(\frac{ayx^2z)/2)	\frac{\partial\:}{\partial\:x}(\frac{ayx^{2}z}{2})
integral of (x^4+x^2)	\int\:(x^{4}+x^{2})dx
limit as x approaches 0 of 2/(e^x+1)	\lim\:_{x\to\:0}(\frac{2}{e^{x}+1})
sum from n=1 to infinity of 3/(n(n+2))	\sum\:_{n=1}^{\infty\:}\frac{3}{n(n+2)}
(\partial)/(\partial x)(-4sin(3x))	\frac{\partial\:}{\partial\:x}(-4\sin(3x))
(\partial)/(\partial x)(x/(x^3y^6))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{3}y^{6}})
derivative of xcos(x+pi)	\frac{d}{dx}(x\cos(x)+π)
y^{''}-2y^'-3y=-5te-t	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=-5te-t
derivative of sqrt(3x+5)	derivative\:\sqrt{3x+5}
y^'+6(tan(6x))y=4cos(6x)	y^{\prime\:}+6(\tan(6x))y=4\cos(6x)
integral of sin(x)e^{-2x}	\int\:\sin(x)e^{-2x}dx
integral of (5x^3+7x+2)/(x^4+9x^2)	\int\:\frac{5x^{3}+7x+2}{x^{4}+9x^{2}}dx
inverse oflaplace 2/((s+1)(s+2))	inverselaplace\:\frac{2}{(s+1)(s+2)}
(\partial)/(\partial u)(sin^2(u))	\frac{\partial\:}{\partial\:u}(\sin^{2}(u))
tangent of 18cos(x)+9sin(2x)	tangent\:18\cos(x)+9\sin(2x)
integral from 0 to 4pi of sqrt(1/2)	\int\:_{0}^{4π}\sqrt{\frac{1}{2}}
sum from n=1 to infinity of (n^2)/(6^n)	\sum\:_{n=1}^{\infty\:}\frac{n^{2}}{6^{n}}
normal of y=7xe^x,(0,0)	normal\:y=7xe^{x},(0,0)
derivative of y=sqrt(1/(t(8t+1)))	derivative\:y=\sqrt{\frac{1}{t(8t+1)}}
area 2x^2,5x-3x^2	area\:2x^{2},5x-3x^{2}
y^'=(1-7x)y^2	y^{\prime\:}=(1-7x)y^{2}
integral of tan^5(2x)	\int\:\tan^{5}(2x)dx
integral from-1 to 2 of (x^3-2x)	\int\:_{-1}^{2}(x^{3}-2x)dx
derivative of f(x)=(csc(x))/x	derivative\:f(x)=\frac{\csc(x)}{x}
integral of x^2cos(1/7 x)	\int\:x^{2}\cos(\frac{1}{7}x)dx
y^{''}-4y^'=7-3e^{4x}	y^{\prime\:\prime\:}-4y^{\prime\:}=7-3e^{4x}
limit as x approaches-pi-of (x+pi)csc(x)	\lim\:_{x\to\:-π-}((x+π)\csc(x))
integral of (2x)/(4x^2+1)	\int\:\frac{2x}{4x^{2}+1}dx
integral of 1/((1+y^2))	\int\:\frac{1}{(1+y^{2})}dy
derivative of y=axsqrt(1-x)	derivative\:y=ax\sqrt{1-x}
integral of (5x-2)e^{2x}	\int\:(5x-2)e^{2x}dx
integral of 4x+8	\int\:4x+8dx
integral of (200)/(t^2+3t+2)	\int\:\frac{200}{t^{2}+3t+2}dt
integral of (3x^3)/(sqrt(5-9x^4))	\int\:\frac{3x^{3}}{\sqrt{5-9x^{4}}}dx
integral of (x^2+6x+2)/(x^3+9x^2+6x+3)	\int\:\frac{x^{2}+6x+2}{x^{3}+9x^{2}+6x+3}dx
tangent of-3cos(x),\at x=-pi/3	tangent\:-3\cos(x),\at\:x=-\frac{π}{3}
maclaurin e^{2x^3}	maclaurin\:e^{2x^{3}}
(\partial)/(\partial y)(4x^3y^2-1)	\frac{\partial\:}{\partial\:y}(4x^{3}y^{2}-1)
laplacetransform cos^2(13t)	laplacetransform\:\cos^{2}(13t)
derivative of y=ln(5)	derivative\:y=\ln(5)
(dy)/(dx)=5cos^3(3x+6)	\frac{dy}{dx}=5\cos^{3}(3x+6)
integral of (x^3)/(sqrt(x^2-16))	\int\:\frac{x^{3}}{\sqrt{x^{2}-16}}dx
integral from 1 to 2 of (12)/(x^2)-1	\int\:_{1}^{2}\frac{12}{x^{2}}-1dx
derivative of ln(4^x)	\frac{d}{dx}(\ln(4^{x}))
integral of 6/(x^2sqrt(x^2+9))	\int\:\frac{6}{x^{2}\sqrt{x^{2}+9}}dx
dx=e^{3x}dy	dx=e^{3x}dy
integral of s8^s	\int\:s8^{s}ds
integral of (x^2)/(x^2+2)	\int\:\frac{x^{2}}{x^{2}+2}dx
derivative of y=sqrt(3-6x)	derivative\:y=\sqrt{3-6x}
(\partial)/(\partial x)(x^2cos(x))	\frac{\partial\:}{\partial\:x}(x^{2}\cos(x))
y^'+xy=1	y^{\prime\:}+xy=1
integral of 1+2sin(x)+sin^2(x)	\int\:1+2\sin(x)+\sin^{2}(x)dx
integral of 2^xtan(3-2^x)	\int\:2^{x}\tan(3-2^{x})dx
2sqrt(xy)(dy)/(dx)=5	2\sqrt{xy}\frac{dy}{dx}=5
limit as x approaches 2 of 3x+4	\lim\:_{x\to\:2}(3x+4)
f(t)=sin(t)	f(t)=\sin(t)
derivative of {f}(x(sin(x)))	\frac{d}{dx}({f}(x)(\sin(x)))
derivative of xln(sin(x))	\frac{d}{dx}(x\ln(\sin(x)))
integral from 0 to infinity of e^{-x}	\int\:_{0}^{\infty\:}e^{-x}dx
integral of xcos(x^2)	\int\:x\cos(x^{2})dx
derivative of f(x)=9+3/x	derivative\:f(x)=9+\frac{3}{x}
integral of (x/(x^2+4))	\int\:(\frac{x}{x^{2}+4})dx
limit as x approaches 0-of (2^x-1)/x	\lim\:_{x\to\:0-}(\frac{2^{x}-1}{x})

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