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Popular Calculus Problems

derivative of 2x^2+5	\frac{d}{dx}(2x^{2}+5)
derivative of y=cot^2(cos(x))	derivative\:y=\cot^{2}(\cos(x))
d/(dt)(t/(t-2))	\frac{d}{dt}(\frac{t}{t-2})
integral of (-1-u)/(u^3+u^2-8u-12)	\int\:\frac{-1-u}{u^{3}+u^{2}-8u-12}du
integral of 2x^2+3	\int\:2x^{2}+3dx
derivative of-(13/(x^4))	\frac{d}{dx}(-\frac{13}{x^{4}})
derivative of f(x)=(12)/((3x-4)^5)	\frac{d}{dx}f(x)=\frac{12}{(3x-4)^{5}}
integral of (-2)/(z^3)	\int\:\frac{-2}{z^{3}}dz
derivative of (3x-y^2)	\frac{d}{dx}((3x-y)^{2})
integral of (x+1)(x-2)^9	\int\:(x+1)(x-2)^{9}dx
y^{''}+4y^'+5y=15x+e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=15x+e^{-x}
derivative of (sin(x)/(1+sin(x)))	\frac{d}{dx}(\frac{\sin(x)}{1+\sin(x)})
integral of (xln(x))/(sqrt(x^2-1))	\int\:\frac{x\ln(x)}{\sqrt{x^{2}-1}}dx
integral from 1 to infinity of (1/(x^3))	\int\:_{1}^{\infty\:}(\frac{1}{x^{3}})dx
(dy)/(dx)x+y=-2x^6y^4	\frac{dy}{dx}x+y=-2x^{6}y^{4}
4(d^2x)/(dt^2)-1(dx)/(dt)-3x=0,x(0)=1	4\frac{d^{2}x}{dt^{2}}-1\frac{dx}{dt}-3x=0,x(0)=1
derivative of arctan(-6x)	derivative\:\arctan(-6x)
laplacetransform 4t^2cos(2t)+5te^{-7t}	laplacetransform\:4t^{2}\cos(2t)+5te^{-7t}
derivative of \sqrt[4]{x^9}+2sqrt(x^5)	\frac{d}{dx}(\sqrt[4]{x^{9}}+2\sqrt{x^{5}})
derivative of f(x)=(c^5-x^5)/(c^5+c^5)	derivative\:f(x)=\frac{c^{5}-x^{5}}{c^{5}+c^{5}}
f^'(t)-f(t)=6t	f^{\prime\:}(t)-f(t)=6t
y^2+x^2y^'=xyy^'	y^{2}+x^{2}y^{\prime\:}=xyy^{\prime\:}
integral of 8sin^2(t-pi/(12))	\int\:8\sin^{2}(t-\frac{π}{12})dt
derivative of 2sin^2(t)	derivative\:2\sin^{2}(t)
taylor f(x)= x/(e^x-1)	taylor\:f(x)=\frac{x}{e^{x}-1}
integral from 9 to 16 of 1/(8-sqrt(x))	\int\:_{9}^{16}\frac{1}{8-\sqrt{x}}dx
area y=x,y=(x-1)^2	area\:y=x,y=(x-1)^{2}
integral of ((ln(x))^{42})/x	\int\:\frac{(\ln(x))^{42}}{x}dx
integral of ((9+sqrt(x)+x))/x	\int\:\frac{(9+\sqrt{x}+x)}{x}dx
derivative of (e^{2x}-5x^2)	\frac{d}{dx}((e^{2x}-5x)^{2})
integral of sec^2(2x)sin(2x)	\int\:\sec^{2}(2x)\sin(2x)dx
limit as x approaches-infinity of g(x)	\lim\:_{x\to\:-\infty\:}(g(x))
integral of 13sin^6(x)cos^3(x)	\int\:13\sin^{6}(x)\cos^{3}(x)dx
integral from 0 to 2 of pi(16-y^4)	\int\:_{0}^{2}π(16-y^{4})dy
derivative of (1+(10/x)^x)	\frac{d}{dx}((1+\frac{10}{x})^{x})
derivative of cos(t)+tsin(t)	derivative\:\cos(t)+t\sin(t)
integral of sqrt(6x-7)	\int\:\sqrt{6x-7}dx
derivative of In^3x	\frac{d}{dx}(In^{3}x)
integral of (ln(9x^2-1))/(x^3)	\int\:\frac{\ln(9x^{2}-1)}{x^{3}}dx
derivative of 3x^2+5	derivative\:3x^{2}+5
derivative of-2x^2	derivative\:-2x^{2}
(\partial)/(\partial x)(x/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+y^{2}})
(\partial)/(\partial x)(x^2y^2+z^2)	\frac{\partial\:}{\partial\:x}(x^{2}y^{2}+z^{2})
16y^{''}+3y=0	16y^{\prime\:\prime\:}+3y=0
y^{''}+20y^'+200=300	y^{\prime\:\prime\:}+20y^{\prime\:}+200=300
integral from 0 to N of e^{-st}sin(2t)	\int\:_{0}^{N}e^{-st}\sin(2t)dt
derivative of 1/(sqrt(1+4t^2))	derivative\:\frac{1}{\sqrt{1+4t^{2}}}
tangent of (4x)/(x+1)(3.3)	tangent\:\frac{4x}{x+1}(3.3)
derivative of y=t(ln(3t))^2	derivative\:y=t(\ln(3t))^{2}
derivative of sqrt(x^3+2)	\frac{d}{dx}(\sqrt{x^{3}+2})
slope of 5/(sqrt(x))	slope\:\frac{5}{\sqrt{x}}
integral of 10x^{3/2}	\int\:10x^{\frac{3}{2}}dx
integral of (e^{-x}-e^2)*(e^x+e^{-5})	\int\:(e^{-x}-e^{2})\cdot\:(e^{x}+e^{-5})dx
integral from 0 to 1 of 3^{-x}	\int\:_{0}^{1}3^{-x}dx
limit as x approaches-infinity of x^2-3	\lim\:_{x\to\:-\infty\:}(x^{2}-3)
tangent of 2x^3+5x^2-4x-12	tangent\:2x^{3}+5x^{2}-4x-12
integral from b to 2b of x^6	\int\:_{b}^{2b}x^{6}dx
integral of cot^3(9x)	\int\:\cot^{3}(9x)dx
integral from 1 to e of ln(23x)	\int\:_{1}^{e}\ln(23x)dx
derivative of-4x+4	\frac{d}{dx}(-4x+4)
derivative of 8xe^{-x}	\frac{d}{dx}(8xe^{-x})
limit as x approaches 0 of 1-e^x	\lim\:_{x\to\:0}(1-e^{x})
derivative of asin(3x)	\frac{d}{dx}(a\sin(3x))
derivative of 2ysin(x)	\frac{d}{dx}(2y\sin(x))
integral of 1/(e^2)	\int\:\frac{1}{e^{2}}dx
limit as x approaches-1-of x/(x^2-1)	\lim\:_{x\to\:-1-}(\frac{x}{x^{2}-1})
limit as x approaches infinity of 2e^x	\lim\:_{x\to\:\infty\:}(2e^{x})
slope of (6,6),(-10,-7)	slope\:(6,6),(-10,-7)
d/(dt)(e^t+e^{-t}+t)	\frac{d}{dt}(e^{t}+e^{-t}+t)
integral of 7/(θ^2)cos(7/θ)	\int\:\frac{7}{θ^{2}}\cos(\frac{7}{θ})dθ
(\partial)/(\partial x)(1-1/x)	\frac{\partial\:}{\partial\:x}(1-\frac{1}{x})
derivative of 1/(8x)	derivative\:\frac{1}{8x}
slope of y=sqrt(x),(25,5)	slope\:y=\sqrt{x},(25,5)
f(x)=sqrt(x)+7/(sqrt(x))	f(x)=\sqrt{x}+\frac{7}{\sqrt{x}}
limit as x approaches 0 of 7^x	\lim\:_{x\to\:0}(7^{x})
derivative of f(x)	derivative\:f(x)
(\partial)/(\partial y)(sqrt(4-x^2-y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{4-x^{2}-y^{2}})
integral from 0 to pi of cos^3(2x)	\int\:_{0}^{π}\cos^{3}(2x)dx
integral of sqrt(1+\sqrt{z)}	\int\:\sqrt{1+\sqrt{z}}dz
integral of (x-2)^4	\int\:(x-2)^{4}dx
derivative of (5^{2/3}-x^{2/3}^{3/2})	\frac{d}{dx}((5^{\frac{2}{3}}-x^{\frac{2}{3}})^{\frac{3}{2}})
derivative of e(1/x)	\frac{d}{dx}(e(\frac{1}{x}))
derivative of (e^{-2x}/x)	\frac{d}{dx}(\frac{e^{-2x}}{x})
16xy^'-2y=-(x^2)/(y^{15)}	16xy^{\prime\:}-2y=-\frac{x^{2}}{y^{15}}
maclaurin tan(2x)	maclaurin\:\tan(2x)
integral of (((1+4ln(x))^5)/x)	\int\:(\frac{(1+4\ln(x))^{5}}{x})dx
integral of (e^{4x}+3)/(e^{3x)}	\int\:\frac{e^{4x}+3}{e^{3x}}dx
derivative of x^2-y^2	\frac{d}{dx}(x^{2}-y^{2})
integral of cos^2(wt)	\int\:\cos^{2}(wt)dt
limit as x approaches-3 of x/x+1/3	\lim\:_{x\to\:-3}(\frac{x}{x}+\frac{1}{3})
derivative of xln\|cos(x\|)	\frac{d}{dx}(x\ln\left\|\cos(x)\right\|)
integral of (sin(8x))/8	\int\:\frac{\sin(8x)}{8}dx
integral of (13)/((1-x^2)^{3/2)}	\int\:\frac{13}{(1-x^{2})^{\frac{3}{2}}}dx
(dy)/(dx)=ye^{-x^2},y(4)=1	\frac{dy}{dx}=ye^{-x^{2}},y(4)=1
y^2(dy)/(dx)=3x^2y^3-6x^2	y^{2}\frac{dy}{dx}=3x^{2}y^{3}-6x^{2}
(2dx)/(dt)+3x=0,x(0)=5	\frac{2dx}{dt}+3x=0,x(0)=5
integral of sin^5(6x)	\int\:\sin^{5}(6x)dx
laplacetransform sin(6t)	laplacetransform\:\sin(6t)
(dy}{dx}-y/x =y^2\frac{sin(x))/x	\frac{dy}{dx}-\frac{y}{x}=y^{2}\frac{\sin(x)}{x}
integral from 0 to 4 of 4e^{-3x}	\int\:_{0}^{4}4e^{-3x}dx

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