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Popular Calculus Problems

integral from-2 to 2 of sqrt(2+\|x\|)	\int\:_{-2}^{2}\sqrt{2+\left\|x\right\|}dx
derivative of x^2(580-x/3)	derivative\:x^{2}(580-\frac{x}{3})
taylor 9.8-y/5	taylor\:9.8-\frac{y}{5}
y^{''}+4y^'+4=0	y^{\prime\:\prime\:}+4y^{\prime\:}+4=0
integral of cos^9(x)tan^8(x)	\int\:\cos^{9}(x)\tan^{8}(x)dx
(\partial)/(\partial x)(3e^x)	\frac{\partial\:}{\partial\:x}(3e^{x})
derivative of f(2)=11x^2+5x	derivative\:f(2)=11x^{2}+5x
tangent of f(x)=x^2-x^4,(1,0)	tangent\:f(x)=x^{2}-x^{4},(1,0)
derivative of ((x+2/x)^3+((x-2)/x)^3)	\frac{d}{dx}((\frac{x+2}{x})^{3}+(\frac{x-2}{x})^{3})
(dx)/(dy)-x/y =2y	\frac{dx}{dy}-\frac{x}{y}=2y
derivative of y=24sqrt(x)	\frac{d}{dx}y=24\sqrt{x}
limit as x approaches 0 of 2xsin(1/x)	\lim\:_{x\to\:0}(2x\sin(\frac{1}{x}))
y^'=(e^y+1)/(e^y)	y^{\prime\:}=\frac{e^{y}+1}{e^{y}}
limit as x approaches 3 of x^3+3x^2-x+2	\lim\:_{x\to\:3}(x^{3}+3x^{2}-x+2)
area x^2-7,6x	area\:x^{2}-7,6x
derivative of 3e^{1-x^2}	\frac{d}{dx}(3e^{1-x^{2}})
f(y)= 1/(y^2)	f(y)=\frac{1}{y^{2}}
y(dy)/(dx)=-x	y\frac{dy}{dx}=-x
integral of cos^3(x/2)sin^2(x/2)	\int\:\cos^{3}(\frac{x}{2})\sin^{2}(\frac{x}{2})dx
laplacetransform t^2+1	laplacetransform\:t^{2}+1
derivative of y=sec(x)-6cos(x)	derivative\:y=\sec(x)-6\cos(x)
derivative of y=x^8+7x^6-5x+4	derivative\:y=x^{8}+7x^{6}-5x+4
derivative of sin^2(x-1)	\frac{d}{dx}(\sin^{2}(x-1))
integral of (2x^2-1)(2x^3-3x+9)^{1/3}	\int\:(2x^{2}-1)(2x^{3}-3x+9)^{\frac{1}{3}}dx
((x^2))/(y^2-5)y^'= 1/(2y)	\frac{(x^{2})}{y^{2}-5}y^{\prime\:}=\frac{1}{2y}
integral from 6 to 7 of t^2	\int\:_{6}^{7}t^{2}dt
limit as x approaches 2 of sqrt(f(x))	\lim\:_{x\to\:2}(\sqrt{f(x)})
derivative of f(x)=(0.3(9^x))/(x^3)	derivative\:f(x)=\frac{0.3(9^{x})}{x^{3}}
y^{''}-4y^'+4y=(12x^2-6x)e^2x	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=(12x^{2}-6x)e^{2}x
sum from n=1 to infinity of (8^n)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{8^{n}}{n!}
integral of x/(3x+2)	\int\:\frac{x}{3x+2}dx
tangent of 8x-x^2	tangent\:8x-x^{2}
derivative of x^6sin(x)	\frac{d}{dx}(x^{6}\sin(x))
sum from n=0 to infinity of 1/(101^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{101^{n}}
area (sqrt(x))/4 ,25,0,12	area\:\frac{\sqrt{x}}{4},25,0,12
derivative of sqrt(x^2-4)sqrt(x+3)	\frac{d}{dx}(\sqrt{x^{2}-4}\sqrt{x+3})
inverse oflaplace e^{-4s}	inverselaplace\:e^{-4s}
(\partial)/(\partial z)(-9cos(3x+yz)z)	\frac{\partial\:}{\partial\:z}(-9\cos(3x+yz)z)
sum from n=1 to infinity of ne^{-5n}	\sum\:_{n=1}^{\infty\:}ne^{-5n}
derivative of cos^4(θ+9)	derivative\:\cos^{4}(θ+9)
tangent of y=x^4+4e^x,(0,4)	tangent\:y=x^{4}+4e^{x},(0,4)
derivative of ((1-2x/(1+x))^3)	\frac{d}{dx}((\frac{1-2x}{1+x})^{3})
derivative of (4x/(7-tan(x)))	\frac{d}{dx}(\frac{4x}{7-\tan(x)})
integral from 0 to 5 of 1/(x^{17/16)}	\int\:_{0}^{5}\frac{1}{x^{\frac{17}{16}}}dx
derivative of [tan(x^{2/3})]^3	derivative\:[\tan(x^{\frac{2}{3}})]^{3}
integral of (x-1)/((x-1)^2+1)	\int\:\frac{x-1}{(x-1)^{2}+1}dx
derivative of f(t)=sqrt(7+10x)	derivative\:f(t)=\sqrt{7+10x}
derivative of 5xln(x)	\frac{d}{dx}(5x\ln(x))
integral of 1/(sqrt(5x-3))	\int\:\frac{1}{\sqrt{5x-3}}dx
limit as h approaches 0 of ((2^h-1))/h	\lim\:_{h\to\:0}(\frac{(2^{h}-1)}{h})
derivative of (3+2xe^{-2x})	\frac{d}{dx}((3+2x)e^{-2x})
derivative of pix^2	\frac{d}{dx}(πx^{2})
integral of (x^2+24x^3)/x	\int\:\frac{x^{2}+24x^{3}}{x}dx
derivative of arcsinh(5x^3-4x^2+11)	\frac{d}{dx}(\arcsinh(5x^{3}-4x^{2}+11))
tangent of f(x)=2x-1+6/x ,\at x=2	tangent\:f(x)=2x-1+\frac{6}{x},\at\:x=2
(\partial)/(\partial x)(A(e^{2x}+2e^{2x}x))	\frac{\partial\:}{\partial\:x}(A(e^{2x}+2e^{2x}x))
tangent of (x^2+y^2)^3=8x^2y^2,(1,1)	tangent\:(x^{2}+y^{2})^{3}=8x^{2}y^{2},(1,1)
(\partial)/(\partial x)(x^2+y^2-z^2)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}-z^{2})
integral from-2 to-1 of 4/(x^2)	\int\:_{-2}^{-1}\frac{4}{x^{2}}dx
slope of (13)(1-10)	slope\:(13)(1-10)
derivative of sqrt(3)e^x	derivative\:\sqrt{3}e^{x}
integral from 2 to 4 of (sqrt(x^2-4))/x	\int\:_{2}^{4}\frac{\sqrt{x^{2}-4}}{x}dx
derivative of e^tsin(4t)	derivative\:e^{t}\sin(4t)
integral of sin^5(2x)cos(2x)	\int\:\sin^{5}(2x)\cos(2x)dx
integral of (2x+1)/(x^2+2x-3)	\int\:\frac{2x+1}{x^{2}+2x-3}dx
integral of e^{-2kx}	\int\:e^{-2kx}dx
derivative of y=sqrt(7+9x)	derivative\:y=\sqrt{7+9x}
derivative of 5sec(x-10cos(x))	\frac{d}{dx}(5\sec(x)-10\cos(x))
(x^2+3)y^'=xy	(x^{2}+3)y^{\prime\:}=xy
tangent of (x^3-9x)^{12}	tangent\:(x^{3}-9x)^{12}
x((dy)/(dx))-y=3x^4	x(\frac{dy}{dx})-y=3x^{4}
implicit (dy)/(dx),7sin(x)+cos(y)=sin(x)cos(y)	implicit\:\frac{dy}{dx},7\sin(x)+\cos(y)=\sin(x)\cos(y)
integral of 3x^5-x^3+6	\int\:3x^{5}-x^{3}+6dx
derivative of f(x)=e^xx+2e^x	derivative\:f(x)=e^{x}x+2e^{x}
limit as x approaches 3 of (x^2-x-6)/(x^2-5x+6)	\lim\:_{x\to\:3}(\frac{x^{2}-x-6}{x^{2}-5x+6})
derivative of xcos(sqrt(x-3))	derivative\:x\cos(\sqrt{x-3})
derivative of (4x^2-5x+9)/(3x+7)	derivative\:\frac{4x^{2}-5x+9}{3x+7}
limit as x approaches 2 of x^2-3x-4	\lim\:_{x\to\:2}(x^{2}-3x-4)
y^'=e^{(t+y)}	y^{\prime\:}=e^{(t+y)}
(dy)/(dx)=cos^2(+sin(2x))	\frac{dy}{dx}=\cos^{2}(+\sin(2x))
integral of (x+7)e^{2x+3}	\int\:(x+7)e^{2x+3}dx
integral from-2 to 3 of (33)/(x^4)	\int\:_{-2}^{3}\frac{33}{x^{4}}dx
integral of x^3-6x^2+x+3	\int\:x^{3}-6x^{2}+x+3dx
limit as x approaches-7 of (x^2-5)/(7-x)	\lim\:_{x\to\:-7}(\frac{x^{2}-5}{7-x})
integral of (cos(x))/(sin(x)+cos(x))	\int\:\frac{\cos(x)}{\sin(x)+\cos(x)}dx
derivative of (1+3x^{1/(2x)})	\frac{d}{dx}((1+3x)^{\frac{1}{2x}})
((3y^2-t^2))/(y^5)((dy)/(dt))+t/(2y^4)=0	\frac{(3y^{2}-t^{2})}{y^{5}}(\frac{dy}{dt})+\frac{t}{2y^{4}}=0
tangent of sqrt(x),\at x=9	tangent\:\sqrt{x},\at\:x=9
(\partial)/(\partial y)(4y)	\frac{\partial\:}{\partial\:y}(4y)
slope of (10,5),(1,12)	slope\:(10,5),(1,12)
inverse oflaplace 1/(s^3+1)	inverselaplace\:\frac{1}{s^{3}+1}
limit as x approaches 0 of x*e^{-1/x}	\lim\:_{x\to\:0}(x\cdot\:e^{-\frac{1}{x}})
integral of (x^2)/((x+1)^4)	\int\:\frac{x^{2}}{(x+1)^{4}}dx
limit as x approaches 0 of x-4/(x^2)	\lim\:_{x\to\:0}(x-\frac{4}{x^{2}})
derivative of arcsech(sin(x))	\frac{d}{dx}(\arcsech(\sin(x)))
integral of e^xx^4	\int\:e^{x}x^{4}dx
d/(dθ)(a^2sin^2(θ)+b^2cos^2(θ))	\frac{d}{dθ}(a^{2}\cdot\:\sin^{2}(θ)+b^{2}\cdot\:\cos^{2}(θ))
f(x)=sin^{11}(x)	f(x)=\sin^{11}(x)
(dy)/(dx)=-6(y^2-y)	\frac{dy}{dx}=-6(y^{2}-y)
derivative of (2ln(2x))/(2-3x)	derivative\:\frac{2\ln(2x)}{2-3x}

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