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Popular Calculus Problems

derivative of ae^x	\frac{d}{dx}(ae^{x})
derivative of f(x)=(2x+1)(3x-2)	derivative\:f(x)=(2x+1)(3x-2)
integral from 3 to e^4 of 1/x	\int\:_{3}^{e^{4}}\frac{1}{x}dx
area y=ln(x),y=0,x=e	area\:y=\ln(x),y=0,x=e
integral of cos(2)(x)	\int\:\cos(2)(x)dx
integral of (8+u)	\int\:(8+u)du
(dy)/(dx)+4y=7	\frac{dy}{dx}+4y=7
(dx)/(dx)	\frac{dx}{dx}
limit as x approaches 2 of x^2-1	\lim\:_{x\to\:2}(x^{2}-1)
integral of tan^5(x)sec^7(x)	\int\:\tan^{5}(x)\sec^{7}(x)dx
derivative of e^{x^2+y^2}	\frac{d}{dx}(e^{x^{2}+y^{2}})
integral of x/(sqrt(x^2-100))	\int\:\frac{x}{\sqrt{x^{2}-100}}dx
derivative of Ae^{-2x}x	\frac{d}{dx}(A\cdot\:e^{-2x}\cdot\:x)
integral of (x^{3/2}+8x+2)	\int\:(x^{\frac{3}{2}}+8x+2)dx
derivative of 2arctan(3x-ln(2+3x))	\frac{d}{dx}(2\arctan(3x)-\ln(2+3x))
integral from 3 to 6 of 1/(sqrt(36-x^2))	\int\:_{3}^{6}\frac{1}{\sqrt{36-x^{2}}}dx
derivative of f(t)=ln(cos(t))	derivative\:f(t)=\ln(\cos(t))
tangent of f(x)=e^xcos(x),(0,1)	tangent\:f(x)=e^{x}\cos(x),(0,1)
(\partial)/(\partial x)(ln(7x^2+y^2+6))	\frac{\partial\:}{\partial\:x}(\ln(7x^{2}+y^{2}+6))
xy^'+2y=-2e^x	xy^{\prime\:}+2y=-2e^{x}
limit as x approaches-3 of 7/(x+3)	\lim\:_{x\to\:-3}(\frac{7}{x+3})
y^'=t^2-y	y^{\prime\:}=t^{2}-y
derivative of arccos(3/x)	\frac{d}{dx}(\arccos(\frac{3}{x}))
7y^{''}+4y^'=0	7y^{\prime\:\prime\:}+4y^{\prime\:}=0
integral of (t^2+2)^3	\int\:(t^{2}+2)^{3}dt
d/(dt)(6sin(t))	\frac{d}{dt}(6\sin(t))
tangent of y=4x^2	tangent\:y=4x^{2}
limit as x approaches-2 of (x^2-1)(7x+3)	\lim\:_{x\to\:-2}((x^{2}-1)(7x+3))
inverse oflaplace 1/(s^2(s-1))	inverselaplace\:\frac{1}{s^{2}(s-1)}
integral of (3e^x+5sec^2(x))	\int\:(3e^{x}+5\sec^{2}(x))dx
(\partial)/(\partial y)((2y)/(x+z))	\frac{\partial\:}{\partial\:y}(\frac{2y}{x+z})
derivative of 8(x^3-x^4)	\frac{d}{dx}(8(x^{3}-x)^{4})
derivative of f(x)=1.58e^{-0.213x}	derivative\:f(x)=1.58e^{-0.213x}
derivative of f(x)=(4x)/(e^x)	derivative\:f(x)=\frac{4x}{e^{x}}
derivative of sqrt(35x)ln(20x)	derivative\:\sqrt{35x}\ln(20x)
integral of (15x^{-2}-5x)cos(6x^{-1}+x^2)	\int\:(15x^{-2}-5x)\cos(6x^{-1}+x^{2})dx
integral of 2^s	\int\:2^{s}ds
(dy)/(dx)=y-3	\frac{dy}{dx}=y-3
y^{''}-10y^'+y=0	y^{\prime\:\prime\:}-10y^{\prime\:}+y=0
integral of (24y-14)/(6y^2-7y)	\int\:\frac{24y-14}{6y^{2}-7y}dy
inverse oflaplace 1/(s(s+1))-1/(s+1)	inverselaplace\:\frac{1}{s(s+1)}-\frac{1}{s+1}
integral of 1/(x^2)sqrt(6+1/x)	\int\:\frac{1}{x^{2}}\sqrt{6+\frac{1}{x}}dx
limit as x approaches 0 of cot(4x)	\lim\:_{x\to\:0}(\cot(4x))
derivative of (2x^2-1/(x^3-x))	\frac{d}{dx}(\frac{2x^{2}-1}{x^{3}-x})
derivative of 1/(2sqrt(r))+1/(9r^{(8/9))}	derivative\:\frac{1}{2\sqrt{r}}+\frac{1}{9r^{(\frac{8}{9})}}
limit as x approaches 0 of 1/(3x^3)	\lim\:_{x\to\:0}(\frac{1}{3x^{3}})
y^{''}-2y^'+y=t^{sqrt(3)}e^t	y^{\prime\:\prime\:}-2y^{\prime\:}+y=t^{\sqrt{3}}e^{t}
derivative of 4x^2cos(3x)	\frac{d}{dx}(4x^{2}\cos(3x))
y^{''}-4y^'+4y=xe^{2x}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=xe^{2x}
derivative of (1+x+x^2^{99})	\frac{d}{dx}((1+x+x^{2})^{99})
(\partial)/(\partial u)((u^2+v^2)^{3/2})	\frac{\partial\:}{\partial\:u}((u^{2}+v^{2})^{\frac{3}{2}})
limit as x approaches 4-of 1/(x-4)	\lim\:_{x\to\:4-}(\frac{1}{x-4})
integral of (x^2-1)^{-1}	\int\:(x^{2}-1)^{-1}dx
implicit x^2+2y^2=2	implicit\:x^{2}+2y^{2}=2
area x^2+x-2,[-3,4]	area\:x^{2}+x-2,[-3,4]
integral from 1 to 2 of 3x^4ln(x)	\int\:_{1}^{2}3x^{4}\ln(x)dx
(\partial)/(\partial x)(y/z)	\frac{\partial\:}{\partial\:x}(\frac{y}{z})
derivative of x^3-5/x+4	\frac{d}{dx}(x^{3}-\frac{5}{x}+4)
integral of 2/(3\sqrt[3]{t)}-3/(1+t^2)	\int\:\frac{2}{3\sqrt[3]{t}}-\frac{3}{1+t^{2}}dt
derivative of 200	\frac{d}{dx}(200)
slope of xsqrt(x)	slope\:x\sqrt{x}
derivative of ae^{-x}	\frac{d}{dx}(ae^{-x})
(\partial)/(\partial x)(e^{6y}sin(-6x))	\frac{\partial\:}{\partial\:x}(e^{6y}\sin(-6x))
sum from n=1 to infinity of 17-7/(n^3)	\sum\:_{n=1}^{\infty\:}17-\frac{7}{n^{3}}
integral of sinh(x)cosh^4(x)	\int\:\sinh(x)\cosh^{4}(x)dx
area y=2x^2,y=3-x	area\:y=2x^{2},y=3-x
integral of (5x^2+2/(x^4)-3\sqrt[3]{x})	\int\:(5x^{2}+\frac{2}{x^{4}}-3\sqrt[3]{x})dx
limit as x approaches 5 of (4x)/(x-5)	\lim\:_{x\to\:5}(\frac{4x}{x-5})
y^'=(t+y)^2-1,y(3)=6	y^{\prime\:}=(t+y)^{2}-1,y(3)=6
integral of ((x^2+3x-4))/(x^3-4x^2+4x)	\int\:\frac{(x^{2}+3x-4)}{x^{3}-4x^{2}+4x}dx
area y=4x^2,x=1,y=0	area\:y=4x^{2},x=1,y=0
inverse oflaplace (2e^{-2s})/(5s^2+45)	inverselaplace\:\frac{2e^{-2s}}{5s^{2}+45}
derivative of y=e^{((3x^2))/2}	derivative\:y=e^{\frac{(3x^{2})}{2}}
derivative of (x^{63}-1)/(x-1)	derivative\:\frac{x^{63}-1}{x-1}
derivative of 3/(3x+1)	\frac{d}{dx}(\frac{3}{3x+1})
limit as x approaches infinity of 1/e	\lim\:_{x\to\:\infty\:}(\frac{1}{e})
derivative of y=e^{x^3}	derivative\:y=e^{x^{3}}
(\partial)/(\partial x)(arcsin(xy))	\frac{\partial\:}{\partial\:x}(\arcsin(xy))
derivative of x^2sin^3(3x)	derivative\:x^{2}\sin^{3}(3x)
derivative of x^{10}arctan(x)	derivative\:x^{10}\arctan(x)
(\partial)/(\partial y)(15-5(y+3)^2)	\frac{\partial\:}{\partial\:y}(15-5(y+3)^{2})
(\partial)/(\partial x)(7x^3cos(7x^2y))	\frac{\partial\:}{\partial\:x}(7x^{3}\cos(7x^{2}y))
(\partial)/(\partial y)(3x^4y^2+1)	\frac{\partial\:}{\partial\:y}(3x^{4}y^{2}+1)
integral from-2 to 3 of (22)/(x^4)	\int\:_{-2}^{3}\frac{22}{x^{4}}dx
laplacetransform 1/3	laplacetransform\:\frac{1}{3}
integral of 343x^2cos(7x)	\int\:343x^{2}\cos(7x)dx
tangent of (e^x)/(x+1),\at x=0	tangent\:\frac{e^{x}}{x+1},\at\:x=0
integral of 8cos^4(θ)sin(θ)	\int\:8\cos^{4}(θ)\sin(θ)dθ
integral of 5/(16+x^2)	\int\:\frac{5}{16+x^{2}}dx
derivative of ln(ln(8s))	derivative\:\ln(\ln(8s))
derivative of f(x)=4x^4-x^6	derivative\:f(x)=4x^{4}-x^{6}
derivative of y=(6x^3+3x+1)^{10}	derivative\:y=(6x^{3}+3x+1)^{10}
integral from 0 to 1 of (x+y)	\int\:_{0}^{1}(x+y)dx
integral of (e^tsqrt(e^t+2))/(e^t+6)	\int\:\frac{e^{t}\sqrt{e^{t}+2}}{e^{t}+6}dt
y^{''}-1y^'-12y=0	y^{\prime\:\prime\:}-1y^{\prime\:}-12y=0
(\partial)/(\partial x)(xy-y+sin(1))	\frac{\partial\:}{\partial\:x}(xy-y+\sin(1))
integral from 0 to 2 of 2^{-θ}	\int\:_{0}^{2}2^{-θ}dθ
integral of sin^3(4x)sqrt(cos(4x))	\int\:\sin^{3}(4x)\sqrt{\cos(4x)}dx
(\partial)/(\partial x)(x^{-1}y^2+xy^2+5xy)	\frac{\partial\:}{\partial\:x}(x^{-1}y^{2}+xy^{2}+5xy)
integral from 1 to 16 of 1/(8-sqrt(x))	\int\:_{1}^{16}\frac{1}{8-\sqrt{x}}dx

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