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Popular Calculus Problems

9sqrt(xy)(dy)/(dx)=1	9\sqrt{xy}\frac{dy}{dx}=1
integral of (2x^2+3x-5)sin(x)	\int\:(2x^{2}+3x-5)\sin(x)dx
tangent of f(x)=3x^3-x^2+7,\at x=2	tangent\:f(x)=3x^{3}-x^{2}+7,\at\:x=2
slope of 6x-x^2	slope\:6x-x^{2}
integral from 1 to 5 of x/(sqrt(x-1))	\int\:_{1}^{5}\frac{x}{\sqrt{x-1}}dx
integral of (16x^2)/((sqrt(x^2+9))^5)	\int\:\frac{16x^{2}}{(\sqrt{x^{2}+9})^{5}}dx
integral of-2csc^2(x)cot(x)	\int\:-2\csc^{2}(x)\cot(x)dx
derivative of (5x/(x+3))	\frac{d}{dx}(\frac{5x}{x+3})
d/(dt)(t-(t^3)/3)	\frac{d}{dt}(t-\frac{t^{3}}{3})
integral of (sec^2(x))(2tan(x)+1)	\int\:(\sec^{2}(x))(2\tan(x)+1)dx
(\partial)/(\partial x)(1/4 x^2*y)	\frac{\partial\:}{\partial\:x}(\frac{1}{4}x^{2}\cdot\:y)
(dy}{dx}-(4y)/x =\frac{y^4)/(x^2)	\frac{dy}{dx}-\frac{4y}{x}=\frac{y^{4}}{x^{2}}
(\partial)/(\partial x)(xe^{(x/y)})	\frac{\partial\:}{\partial\:x}(xe^{(\frac{x}{y})})
derivative of f(x)=(x/2)^4	derivative\:f(x)=(\frac{x}{2})^{4}
derivative of f(x)=(x-1)^{2/3}	derivative\:f(x)=(x-1)^{\frac{2}{3}}
sum from n=0 to infinity of x^{4n}	\sum\:_{n=0}^{\infty\:}x^{4n}
derivative of 3ysqrt(xy)	\frac{d}{dx}(3y\sqrt{xy})
integral of 5cos^3(3x)	\int\:5\cos^{3}(3x)dx
integral from-infinity to 1 of xe^x	\int\:_{-\infty\:}^{1}xe^{x}dx
integral of sin(x^2+1)	\int\:\sin(x^{2}+1)dx
integral from-2 to 4 of (-x^2+2x+8)	\int\:_{-2}^{4}(-x^{2}+2x+8)dx
(dy)/(dx)=(sin^2(2x))(cos^2(y))	\frac{dy}{dx}=(\sin^{2}(2x))(\cos^{2}(y))
t(dy)/(dt)=t^3+20t^3y	t\frac{dy}{dt}=t^{3}+20t^{3}y
integral of 1.5sin(-x+2)	\int\:1.5\sin(-x+2)dx
derivative of y=cos(x)-xsin(x)	derivative\:y=\cos(x)-x\sin(x)
f(x)=x^{1/6}	f(x)=x^{\frac{1}{6}}
derivative of sin^8(5x^2+8)	\frac{d}{dx}(\sin^{8}(5x^{2}+8))
integral of (e^{13x})/((e^{13x)+5)^4}	\int\:\frac{e^{13x}}{(e^{13x}+5)^{4}}dx
(dy)/(dx)-0.11y=200	\frac{dy}{dx}-0.11y=200
derivative of (x-3/(2x-5))	\frac{d}{dx}(\frac{x-3}{2x-5})
derivative of-x^2sin(x+4xcos(x)+2sin(x))	\frac{d}{dx}(-x^{2}\sin(x)+4x\cos(x)+2\sin(x))
derivative of sqrt(ln(x^2+4)+xsin(2x))	derivative\:\sqrt{\ln(x^{2}+4)+x\sin(2x)}
derivative of 6x^2+8x+6	\frac{d}{dx}(6x^{2}+8x+6)
integral of x^{15}e^{-x^8}	\int\:x^{15}e^{-x^{8}}dx
integral of (2x+5)(x^2+5x)^7	\int\:(2x+5)(x^{2}+5x)^{7}dx
(dy)/(dx)=(13xy)/((ln(y))^{10)}	\frac{dy}{dx}=\frac{13xy}{(\ln(y))^{10}}
(dh)/(dt)=-h,h(0)=0	\frac{dh}{dt}=-h,h(0)=0
y^'=(5y)/(x+3)	y^{\prime\:}=\frac{5y}{x+3}
limit as x approaches-7 of (x^2-2)/(7-x)	\lim\:_{x\to\:-7}(\frac{x^{2}-2}{7-x})
integral of (4x-1)^2	\int\:(4x-1)^{2}dx
inverse oflaplace 1/(s^2(s+2))	inverselaplace\:\frac{1}{s^{2}(s+2)}
derivative of (log_{10}(x)^2)	\frac{d}{dx}((\log_{10}(x))^{2})
derivative of arctan(sqrt(3x^2-1))	\frac{d}{dx}(\arctan(\sqrt{3x^{2}-1}))
y^{''}+3y=5	y^{\prime\:\prime\:}+3y=5
y^{''}+y= 1/(2k^2)(1+cos(2t))	y^{\prime\:\prime\:}+y=\frac{1}{2k^{2}}(1+\cos(2t))
derivative of (x^5+1^4)	\frac{d}{dx}((x^{5}+1)^{4})
tangent of f(x)= 1/(sqrt(x)),\at x=81	tangent\:f(x)=\frac{1}{\sqrt{x}},\at\:x=81
tangent of arccos(x)+x,\at x=0	tangent\:\arccos(x)+x,\at\:x=0
derivative of y=9+5x^2-2x^3	derivative\:y=9+5x^{2}-2x^{3}
2y^'+4y=2te^{-2t}	2y^{\prime\:}+4y=2te^{-2t}
integral of sqrt((3-x)/(3+x))	\int\:\sqrt{\frac{3-x}{3+x}}dx
integral of (sqrt(ln\|x\|))/x	\int\:\frac{\sqrt{\ln\left\|x\right\|}}{x}dx
integral of 3/(xsqrt(9-(ln(x))^2))	\int\:\frac{3}{x\sqrt{9-(\ln(x))^{2}}}dx
tangent of f(x)=x^2-10x+2,\at x=0	tangent\:f(x)=x^{2}-10x+2,\at\:x=0
limit as x approaches 0 of csc(x)-cot(x)	\lim\:_{x\to\:0}(\csc(x)-\cot(x))
integral of 0.1e^{-0.1x}	\int\:0.1e^{-0.1x}dx
(dy)/(dt)=sin(3t)-2y	\frac{dy}{dt}=\sin(3t)-2y
limit as x approaches 9+of 5/(x-9)	\lim\:_{x\to\:9+}(\frac{5}{x-9})
integral of (5+sqrt(3x+1))	\int\:(5+\sqrt{3x+1})dx
derivative of 3sec(x)	derivative\:3\sec(x)
y^'+y=sin(t)	y^{\prime\:}+y=\sin(t)
derivative of 3+ln(x)	\frac{d}{dx}(3+\ln(x))
inverse oflaplace (e^{-7s})/(s^2)	inverselaplace\:\frac{e^{-7s}}{s^{2}}
integral of 2sin(x^2)	\int\:2\sin(x^{2})dx
integral of (2x-3)/((x-1)^3)	\int\:\frac{2x-3}{(x-1)^{3}}dx
integral of 13tan^5(x)sec^4(x)	\int\:13\tan^{5}(x)\sec^{4}(x)dx
limit as x approaches 5-of (x+1)/(x+5)	\lim\:_{x\to\:5-}(\frac{x+1}{x+5})
integral of 30+cos(x)	\int\:30+\cos(x)dx
slope of (11.5)(2.1)	slope\:(11.5)(2.1)
y^'+4y=5sin(e^{4x})	y^{\prime\:}+4y=5\sin(e^{4x})
integral from 1 to e of 7t^2ln(t)	\int\:_{1}^{e}7t^{2}\ln(t)dt
tangent of x^2+x-3	tangent\:x^{2}+x-3
(\partial)/(\partial y)(3x^2y^4-3)	\frac{\partial\:}{\partial\:y}(3x^{2}y^{4}-3)
derivative of f(x)=4sqrt(x^3)	derivative\:f(x)=4\sqrt{x^{3}}
derivative of ln(1+xy)	\frac{d}{dx}(\ln(1+xy))
integral of 30(x+7)(x+5)^4	\int\:30(x+7)(x+5)^{4}dx
derivative of ln(x/4)	\frac{d}{dx}(\ln(\frac{x}{4}))
sum from n=1 to infinity}(x^{5n of)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{x^{5n}}{n!}
derivative of f(x)=xe^{9x}	derivative\:f(x)=xe^{9x}
limit as x approaches 8 of (8x)/(x-8)	\lim\:_{x\to\:8}(\frac{8x}{x-8})
y^'=(1-2t)y^2,y(0)=-1/6	y^{\prime\:}=(1-2t)y^{2},y(0)=-\frac{1}{6}
integral of x^3sqrt(x^2+24)	\int\:x^{3}\sqrt{x^{2}+24}dx
derivative of (x^2+3/(x+1))	\frac{d}{dx}(\frac{x^{2}+3}{x+1})
integral from 1 to 2 of 5/(2x-1)	\int\:_{1}^{2}\frac{5}{2x-1}dx
integral of 9cos(3x)	\int\:9\cos(3x)dx
integral of x(x+2)^{1/2}	\int\:x(x+2)^{\frac{1}{2}}dx
derivative of sqrt(3x^2-7)	\frac{d}{dx}(\sqrt{3x^{2}-7})
(2xy+3y^2)dx=(2xy+x^2)dy	(2xy+3y^{2})dx=(2xy+x^{2})dy
limit as x approaches 2 of (x^3-8)/(2-x)	\lim\:_{x\to\:2}(\frac{x^{3}-8}{2-x})
integral of (u^2)/(u^2+1)	\int\:\frac{u^{2}}{u^{2}+1}du
sum from k=1 to infinity of k/(2^k)	\sum\:_{k=1}^{\infty\:}\frac{k}{2^{k}}
derivative of cosh(x^2)	\frac{d}{dx}(\cosh(x^{2}))
derivative of \sqrt[5]{(9x^7+3x^4-2)^3}	derivative\:\sqrt[5]{(9x^{7}+3x^{4}-2)^{3}}
(\partial)/(\partial p)(p^3q^2+2pq+p/q)	\frac{\partial\:}{\partial\:p}(p^{3}q^{2}+2pq+\frac{p}{q})
integral of (3x^2)/(x^3-1)	\int\:\frac{3x^{2}}{x^{3}-1}dx
derivative of f(x)=(ln(x^5))^2	derivative\:f(x)=(\ln(x^{5}))^{2}
derivative of-1/2 xcos(x)	\frac{d}{dx}(-\frac{1}{2}x\cos(x))
integral of 9/(x^{-1)+3}	\int\:\frac{9}{x^{-1}+3}dx
(\partial)/(\partial x)(ycos(x^2y))	\frac{\partial\:}{\partial\:x}(y\cos(x^{2}y))
slope of (8 1/7 ,9),(4,3 1/5)	slope\:(8\frac{1}{7},9),(4,3\frac{1}{5})

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