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Popular Calculus Problems

taylor ln((1+x)/(1-x))	taylor\:\ln(\frac{1+x}{1-x})
derivative of log_{5}(sqrt(4x^2+5x-8))	\frac{d}{dx}(\log_{5}(\sqrt{4x^{2}+5x-8}))
(\partial)/(\partial x)(sqrt(xy+y/x))	\frac{\partial\:}{\partial\:x}(\sqrt{xy+\frac{y}{x}})
integral of (cos^5(5x+1))/(sin^4(5x+1))	\int\:\frac{\cos^{5}(5x+1)}{\sin^{4}(5x+1)}dx
tangent of y=((x-1))/(x+1)	tangent\:y=\frac{(x-1)}{x+1}
derivative of-5/(7x+5)	derivative\:-\frac{5}{7x+5}
limit as x approaches 0+of (1+1/x)^x	\lim\:_{x\to\:0+}((1+\frac{1}{x})^{x})
integral of sin(pit)	\int\:\sin(πt)dt
limit as x approaches infinity of x/e	\lim\:_{x\to\:\infty\:}(\frac{x}{e})
integral of cos^3(x/(20))	\int\:\cos^{3}(\frac{x}{20})dx
y^{''}-4y^'=0	y^{\prime\:\prime\:}-4y^{\prime\:}=0
derivative of (xe^t)/(1+xe^t)	derivative\:\frac{xe^{t}}{1+xe^{t}}
limit as h approaches infinity of 2/h+3	\lim\:_{h\to\:\infty\:}(\frac{2}{h}+3)
area 4x^4-4x^2,5x^2,0,1.5	area\:4x^{4}-4x^{2},5x^{2},0,1.5
derivative of \sqrt[9]{x}	derivative\:\sqrt[9]{x}
derivative of sec(x-1/(x^3)+5)	\frac{d}{dx}(\sec(x)-\frac{1}{x^{3}}+5)
limit as x approaches 0 of xln(tan(2x))	\lim\:_{x\to\:0}(x\ln(\tan(2x)))
8y^{''}-8y^'+4y=0	8y^{\prime\:\prime\:}-8y^{\prime\:}+4y=0
(dy)/(dx)=9-(3y)/(250)	\frac{dy}{dx}=9-\frac{3y}{250}
derivative of Y(x)=e^{4x+3}	derivative\:Y(x)=e^{4x+3}
d/(dy)(sqrt(y^2-1))	\frac{d}{dy}(\sqrt{y^{2}-1})
integral of 1/(x^2sqrt(x^2-13))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-13}}dx
(dy)/(dx)=14xe^6x(36+y^2)	\frac{dy}{dx}=14xe^{6}x(36+y^{2})
integral of 9sin^6(x)	\int\:9\sin^{6}(x)dx
y^'+y^3x+9y=0	y^{\prime\:}+y^{3}x+9y=0
integral of x^5+8x^{-3}+2	\int\:x^{5}+8x^{-3}+2dx
derivative of \|3x^3+5x\|	\frac{d}{dx}(\left\|3x^{3}+5x\right\|)
(\partial)/(\partial x)(xy-ln(z))	\frac{\partial\:}{\partial\:x}(xy-\ln(z))
integral of e^{x+y}	\int\:e^{x+y}dy
(\partial)/(\partial s)((s^2+4)/(t-3))	\frac{\partial\:}{\partial\:s}(\frac{s^{2}+4}{t-3})
limit as x approaches 0-of (2x)/(\|x\|)	\lim\:_{x\to\:0-}(\frac{2x}{\left\|x\right\|})
ty^{''}-y^'=t^2+t,y(1)=1,y^'(1)=5	ty^{\prime\:\prime\:}-y^{\prime\:}=t^{2}+t,y(1)=1,y^{\prime\:}(1)=5
slope of (3,-7),(10,-4)	slope\:(3,-7),(10,-4)
derivative of \sqrt[3]{8x^7+9x^6}	\frac{d}{dx}(\sqrt[3]{8x^{7}+9x^{6}})
integral of 1/(x^2-4x+4)	\int\:\frac{1}{x^{2}-4x+4}dx
limit as x approaches 9-of (6x)/(x-9)	\lim\:_{x\to\:9-}(\frac{6x}{x-9})
derivative of (e^{4x}/x)	\frac{d}{dx}(\frac{e^{4x}}{x})
d/(dt)(e^{at})	\frac{d}{dt}(e^{at})
derivative of (6x+4x^2)/((3+4x)^2)	derivative\:\frac{6x+4x^{2}}{(3+4x)^{2}}
y^{''}-y=1	y^{\prime\:\prime\:}-y=1
(dy}{dx}=\frac{8y^2)/x	\frac{dy}{dx}=\frac{8y^{2}}{x}
integral of 5e^{-0.2x}	\int\:5e^{-0.2x}dx
(\partial)/(\partial x)(ln(x-e^xy))	\frac{\partial\:}{\partial\:x}(\ln(x-e^{x}y))
y^{''}+16y=8sin(4t)	y^{\prime\:\prime\:}+16y=8\sin(4t)
integral of 1/(x^2+4x+9)	\int\:\frac{1}{x^{2}+4x+9}dx
y(t+5)(t+2)y^'+t+3=0	y(t+5)(t+2)y^{\prime\:}+t+3=0
derivative of y=(sqrt(x)-10)^{-3}	derivative\:y=(\sqrt{x}-10)^{-3}
derivative of f(x)= x/(x+4)	derivative\:f(x)=\frac{x}{x+4}
integral of 1/((x-1)(x^2+3))	\int\:\frac{1}{(x-1)(x^{2}+3)}dx
integral of ye^{xy}cos(2x)	\int\:ye^{xy}\cos(2x)dx
integral of 3t^2	\int\:3t^{2}dt
d/(d{z)}(({z})/(({x)^2+{y}^2+{z}^2)^{3/2}})	\frac{d}{d{z}}(\frac{{z}}{({x}^{2}+{y}^{2}+{z}^{2})^{\frac{3}{2}}})
derivative of (sin(5x)(arccsc(2)x^3))	\frac{d}{dx}((\sin(5x))(\arccsc(2)x^{3}))
xy^'=y+2x^3sin^2(y/x)	xy^{\prime\:}=y+2x^{3}\sin^{2}(\frac{y}{x})
derivative of sqrt(x^2+100)	\frac{d}{dx}(\sqrt{x^{2}+100})
integral of cos(2x^2)	\int\:\cos(2x^{2})dx
derivative of 1/1	\frac{d}{dx}(\frac{1}{1})
((y-2)dy)/(y+3)=((x-1)dx)/(x+4)	\frac{(y-2)dy}{y+3}=\frac{(x-1)dx}{x+4}
derivative of ln(6x^3+3x^2+3x+3)	derivative\:\ln(6x^{3}+3x^{2}+3x+3)
integral of sin^4(3x)cos^4(3x)	\int\:\sin^{4}(3x)\cos^{4}(3x)dx
tangent of f(x)=9+5x+2xe^x,\at x=0	tangent\:f(x)=9+5x+2xe^{x},\at\:x=0
(\partial)/(\partial y)(2xy^4e^y+2xy^3+y)	\frac{\partial\:}{\partial\:y}(2xy^{4}e^{y}+2xy^{3}+y)
tangent of f(x)=19-x^2,\at x=3	tangent\:f(x)=19-x^{2},\at\:x=3
xy^'-2y^'-(x-2)sin(x)+y=0	xy^{\prime\:}-2y^{\prime\:}-(x-2)\sin(x)+y=0
derivative of (-y/x)	\frac{d}{dx}(\frac{-y}{x})
slope of (-3,7),(2,-5)	slope\:(-3,7),(2,-5)
derivative of f(x)=1-3x^2	derivative\:f(x)=1-3x^{2}
derivative of (2x+3/(3x+2))	\frac{d}{dx}(\frac{2x+3}{3x+2})
cos^2(x)sin(x)(dy)/(dx)+cos^3(x)y=1	\cos^{2}(x)\sin(x)\frac{dy}{dx}+\cos^{3}(x)y=1
tangent of x^3-2x^2-3x	tangent\:x^{3}-2x^{2}-3x
(\partial)/(\partial x)(e^{cos(x-2y)})	\frac{\partial\:}{\partial\:x}(e^{\cos(x-2y)})
inverse oflaplace ((7s+2))/(s^2+6s+34)	inverselaplace\:\frac{(7s+2)}{s^{2}+6s+34}
limit as x approaches 9+of 7/(x-9)	\lim\:_{x\to\:9+}(\frac{7}{x-9})
integral of e^ycos(x)	\int\:e^{y}\cos(x)dx
derivative of (sin(2x))/2	derivative\:\frac{\sin(2x)}{2}
integral from 0 to 3 of x^2-2x	\int\:_{0}^{3}x^{2}-2xdx
derivative of (2-x^{-2})	\frac{d}{dx}((2-x)^{-2})
tangent of y= x/(1+x^2),(2,0.4)	tangent\:y=\frac{x}{1+x^{2}},(2,0.4)
(dy)/(dx)=(x^2y^3)/(x+3)	\frac{dy}{dx}=\frac{x^{2}y^{3}}{x+3}
limit as x approaches 4+of (4-x)/(\|4-x\|)	\lim\:_{x\to\:4+}(\frac{4-x}{\left\|4-x\right\|})
derivative of-5xe^x	\frac{d}{dx}(-5xe^{x})
derivative of e^{5tsin(2t)}	derivative\:e^{5t\sin(2t)}
area e^x,xe^x,0	area\:e^{x},xe^{x},0
(\partial)/(\partial x)(x^2+y^2+z^2-25)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+z^{2}-25)
y^'+2y=2x+e^{4x}	y^{\prime\:}+2y=2x+e^{4x}
integral of 2xcos(9x)	\int\:2x\cos(9x)dx
tangent of f(x)= 3/(x-2),\at x=3	tangent\:f(x)=\frac{3}{x-2},\at\:x=3
integral from 0 to 4 of (3t)/((t-5)^2)	\int\:_{0}^{4}\frac{3t}{(t-5)^{2}}dt
derivative of f(x)= x/(x^2+6)	derivative\:f(x)=\frac{x}{x^{2}+6}
limit as x approaches 2 of 5x^3-9x^2+1	\lim\:_{x\to\:2}(5x^{3}-9x^{2}+1)
limit as x approaches infinity of 4^xx	\lim\:_{x\to\:\infty\:}(4^{x}x)
inverse oflaplace (3s^2)/((s^2+1)^2)	inverselaplace\:\frac{3s^{2}}{(s^{2}+1)^{2}}
integral of ye^{xy}	\int\:y\cdot\:e^{x\cdot\:y}dx
integral of 1/((x+5)^2)	\int\:\frac{1}{(x+5)^{2}}dx
derivative of (-7)/(\sqrt[3]{x)}	derivative\:\frac{-7}{\sqrt[3]{x}}
integral of 2sqrt(x) 1/x	\int\:2\sqrt{x}\frac{1}{x}dx
(\partial)/(\partial x)(e^xln(y))	\frac{\partial\:}{\partial\:x}(e^{x}\ln(y))
y=x^{-2/5}	y=x^{-\frac{2}{5}}
derivative of (3-4x/2)	\frac{d}{dx}(\frac{3-4x}{2})
integral of (x^2)/(sqrt(1-x^6))	\int\:\frac{x^{2}}{\sqrt{1-x^{6}}}dx

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