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Popular Calculus Problems

derivative of 1-e^{-0.1x}	\frac{d}{dx}(1-e^{-0.1x})
slope of (4x+4y)^3=64x^3+64y^3(-1.1)	slope\:(4x+4y)^{3}=64x^{3}+64y^{3}(-1.1)
integral from 2 to 3 of (2x-3)/(sqrt(4x-x^2))	\int\:_{2}^{3}\frac{2x-3}{\sqrt{4x-x^{2}}}dx
y^{''}+2y=sin(sqrt(2)x)	y^{\prime\:\prime\:}+2y=\sin(\sqrt{2}x)
derivative of (2x/2)	\frac{d}{dx}(\frac{2x}{2})
integral of 2sin(x)cos(x)	\int\:2\cdot\:\sin(x)\cdot\:\cos(x)dx
((x^2+1)dy)/(dx)+xy-x=0	\frac{(x^{2}+1)dy}{dx}+xy-x=0
laplacetransform e^{2t}sin(2t)	laplacetransform\:e^{2t}\sin(2t)
integral of sin(t)*cos(t)	\int\:\sin(t)\cdot\:\cos(t)dt
limit as x approaches 2 of 3x^2+2x	\lim\:_{x\to\:2}(3x^{2}+2x)
area x=sqrt(y),x=2-y,y=0	area\:x=\sqrt{y},x=2-y,y=0
derivative of g(x)=x^3-7x^2+2x+40	derivative\:g(x)=x^{3}-7x^{2}+2x+40
derivative of 2e^{-4x}	\frac{d}{dx}(2e^{-4x})
integral of 1/((9x^2+1)^{5/2)}	\int\:\frac{1}{(9x^{2}+1)^{\frac{5}{2}}}dx
volumeabout x=-1,x=y^3,[0,1]	volumeabout\:x=-1,x=y^{3},[0,1]
derivative of sqrt(8+cot^2(x))	\frac{d}{dx}(\sqrt{8+\cot^{2}(x)})
limit as x approaches 2 of 3x^3+x^2-8	\lim\:_{x\to\:2}(3x^{3}+x^{2}-8)
derivative of f(x)=6x^9e^x	derivative\:f(x)=6x^{9}e^{x}
derivative of px+d	derivative\:px+d
derivative of 4xln(x+10)	\frac{d}{dx}(4x\ln(x)+10)
derivative of 4x^2-x+sqrt(x)	\frac{d}{dx}(4x^{2}-x+\sqrt{x})
d/(dt)(ln(sec(t)))	\frac{d}{dt}(\ln(\sec(t)))
(d^2)/(dx^2)(x^2cos(x))	\frac{d^{2}}{dx^{2}}(x^{2}\cos(x))
integral from 1 to 5 of 1/(x-2)	\int\:_{1}^{5}\frac{1}{x-2}dx
sum from n=1 to infinity of 1/(n^{0.5)}	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{0.5}}
d/(dt)(4e^{-3t})	\frac{d}{dt}(4e^{-3t})
d/(dA)(-cos(2)(A)-sin(2)(A))	\frac{d}{dA}(-\cos(2)(A)-\sin(2)(A))
derivative of f(x)=(2x^2+4x+2)/(sqrt(x))	derivative\:f(x)=\frac{2x^{2}+4x+2}{\sqrt{x}}
tangent of f(x)=sin(x),\at x=(7pi)/6	tangent\:f(x)=\sin(x),\at\:x=\frac{7π}{6}
limit as x approaches 2 of (8-x^3)/(x^2-2x)	\lim\:_{x\to\:2}(\frac{8-x^{3}}{x^{2}-2x})
limit as x approaches infinity of (1-x\sqrt[x]{x})/(x-sin(x))	\lim\:_{x\to\:\infty\:}(\frac{1-x\sqrt[x]{x}}{x-\sin(x)})
derivative of 7sin(x-7xcos(x))	\frac{d}{dx}(7\sin(x)-7x\cos(x))
integral from 0 to pi of 2sin(x)	\int\:_{0}^{π}2\sin(x)dx
d/(dθ)(-8sin(θ))	\frac{d}{dθ}(-8\sin(θ))
inverse oflaplace 2/(s+10.04)	inverselaplace\:\frac{2}{s+10.04}
limit as x approaches-infinity of 3-4x^2	\lim\:_{x\to\:-\infty\:}(3-4x^{2})
limit as x approaches infinity of (x^3)/(2^x)	\lim\:_{x\to\:\infty\:}(\frac{x^{3}}{2^{x}})
limit as x approaches-1 of (3+x)/(x^2-1)	\lim\:_{x\to\:-1}(\frac{3+x}{x^{2}-1})
integral of e^{-3x}cos(4x)	\int\:e^{-3x}\cos(4x)dx
integral of (9x^5-3x^2+7)	\int\:(9x^{5}-3x^{2}+7)dx
integral of tan^3(3x)sec(3x)	\int\:\tan^{3}(3x)\sec(3x)dx
integral of (2x+6)/(x^2+1)	\int\:\frac{2x+6}{x^{2}+1}dx
limit as x approaches 2-of 3-x	\lim\:_{x\to\:2-}(3-x)
limit as x approaches 0 of (x^2)cos(7/x)	\lim\:_{x\to\:0}((x^{2})\cos(\frac{7}{x}))
area y=9x^2,y^2= 1/9 x	area\:y=9x^{2},y^{2}=\frac{1}{9}x
integral of x^2e^{12x}	\int\:x^{2}e^{12x}dx
(\partial)/(\partial x)(e^{7xy}ln(4y))	\frac{\partial\:}{\partial\:x}(e^{7xy}\ln(4y))
integral of tan(9x)	\int\:\tan(9x)dx
derivative of-sqrt(x^2+y^2)	\frac{d}{dx}(-\sqrt{x^{2}+y^{2}})
integral of 3x^2arctan(x^3)	\int\:3x^{2}\arctan(x^{3})dx
integral of (e^{3x}sin(2x))	\int\:(e^{3x}\sin(2x))dx
y^{''}-3y^'=8x	y^{\prime\:\prime\:}-3y^{\prime\:}=8x
inverse oflaplace 1/(3s+2)	inverselaplace\:\frac{1}{3s+2}
derivative of (5x)/(x+2)	derivative\:\frac{5x}{x+2}
integral of x^6ln(2x)	\int\:x^{6}\ln(2x)dx
integral from-1 to 1 of (1/(1+x^2))^2	\int\:_{-1}^{1}(\frac{1}{1+x^{2}})^{2}dx
integral of (3x^3-4x^2+3x)/(x^2+1)	\int\:\frac{3x^{3}-4x^{2}+3x}{x^{2}+1}dx
integral of 6x^5-7x^4-9x^2	\int\:6x^{5}-7x^{4}-9x^{2}dx
integral of x+c	\int\:x+cdx
integral from 0 to 1 of integral from 0 to x of (6/7 (x^2+x*y/2))	\int\:_{0}^{1}\int\:_{0}^{x}(\frac{6}{7}(x^{2}+x\cdot\:\frac{y}{2}))dydx
limit as x approaches infinity of ln(9x)-ln(x+7)	\lim\:_{x\to\:\infty\:}(\ln(9x)-\ln(x+7))
integral of 1/(ln(x)x)	\int\:\frac{1}{\ln(x)x}dx
limit as x approaches 19 of (x-19)/(x^2-361)	\lim\:_{x\to\:19}(\frac{x-19}{x^{2}-361})
(dy)/(dx)=e^{2x}-3y,y(0)=2	\frac{dy}{dx}=e^{2x}-3y,y(0)=2
y^{''}+2y^'+y=16e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=16e^{-t}
derivative of sqrt(2x+1)	derivative\:\sqrt{2x+1}
integral from-2 to 3 of (37)/(x^4)	\int\:_{-2}^{3}\frac{37}{x^{4}}dx
area 4x+3,[0,1]	area\:4x+3,[0,1]
f(x)=(sech(2x))^{sin(3x)}	f(x)=(\sech(2x))^{\sin(3x)}
derivative of 1+cos^2(x)	derivative\:1+\cos^{2}(x)
derivative of (3x-2^2(2x+1)^4)	\frac{d}{dx}((3x-2)^{2}(2x+1)^{4})
(\partial)/(\partial x)(4x^2+4y^2)	\frac{\partial\:}{\partial\:x}(4x^{2}+4y^{2})
integral of sqrt(5x+2)	\int\:\sqrt{5x+2}dx
integral from 2 to 9 of (x^3-pix^2)	\int\:_{2}^{9}(x^{3}-πx^{2})dx
tangent of f(x)=8(e^x+e^xx),\at x=0	tangent\:f(x)=8(e^{x}+e^{x}x),\at\:x=0
y^'= x/((1+2y))	y^{\prime\:}=\frac{x}{(1+2y)}
(d^3)/(dx^3)(3t^3-2/(t^2))	\frac{d^{3}}{dx^{3}}(3t^{3}-\frac{2}{t^{2}})
integral of (x^3+x+1/(x^3))	\int\:(x^{3}+x+\frac{1}{x^{3}})dx
integral from 0 to pi/2 of-10sin^2(3x)	\int\:_{0}^{\frac{π}{2}}-10\sin^{2}(3x)dx
integral of x/((sqrt(1+2x)))	\int\:\frac{x}{(\sqrt{1+2x})}dx
derivative of tan(6x^2)	\frac{d}{dx}(\tan(6x^{2}))
(\partial)/(\partial x)(cos^2(x-y))	\frac{\partial\:}{\partial\:x}(\cos^{2}(x-y))
derivative of (x^2/(x-2))	\frac{d}{dx}(\frac{x^{2}}{x-2})
integral from 4 to 6 of 2x	\int\:_{4}^{6}2xdx
d/(dt)(\sqrt[5]{t})	\frac{d}{dt}(\sqrt[5]{t})
integral of 1/(sqrt(16-x))	\int\:\frac{1}{\sqrt{16-x}}dx
(\partial)/(\partial y)(3.5xycos(xyz))	\frac{\partial\:}{\partial\:y}(3.5xy\cos(xyz))
integral of 1/(9x^2-1)	\int\:\frac{1}{9x^{2}-1}dx
integral of 12x^2+2x-6	\int\:12x^{2}+2x-6dx
derivative of 9sec(x)	\frac{d}{dx}(9\sec(x))
derivative of x^4	\frac{d}{dx}(x^{4})
(dy)/(dx)=-x/(4y)	\frac{dy}{dx}=-\frac{x}{4y}
derivative of cot(x^2)	\frac{d}{dx}(\cot(x^{2}))
limit as x approaches pi of (x-pi)csc(x)	\lim\:_{x\to\:π}((x-π)\csc(x))
e^x(ydy)/(dx)=e^{-y}+e^{-2x-y}	e^{x}\frac{ydy}{dx}=e^{-y}+e^{-2x-y}
6y^{''}+y^'-2y=0	6y^{\prime\:\prime\:}+y^{\prime\:}-2y=0
derivative of g(x)=5tan(3x)	derivative\:g(x)=5\tan(3x)
integral of xsin^2(8x)	\int\:x\sin^{2}(8x)dx
integral of 3e^xsin(x)	\int\:3e^{x}\sin(x)dx
limit as x approaches 0 of (3^{sin(x)}-1)/(4x)	\lim\:_{x\to\:0}(\frac{3^{\sin(x)}-1}{4x})

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