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Popular Calculus Problems

limit as x approaches-6 of (\|x+6\|)/(x+6)	\lim\:_{x\to\:-6}(\frac{\left\|x+6\right\|}{x+6})
derivative of 3x^2+3x+cos(x)	\frac{d}{dx}(3x^{2}+3x+\cos(x))
integral of tan^7(x)sec^3(x)	\int\:\tan^{7}(x)\sec^{3}(x)dx
derivative of (sin(x)/(x^2-1))	\frac{d}{dx}(\frac{\sin(x)}{x^{2}-1})
tangent of y=14xsin(x),(pi/2 ,7pi)	tangent\:y=14x\sin(x),(\frac{π}{2},7π)
limit as x approaches infinity of xx	\lim\:_{x\to\:\infty\:}(xx)
integral of 3cos^3(6x)	\int\:3\cos^{3}(6x)dx
integral of cos^{10}(2y)sin^3(2y)	\int\:\cos^{10}(2y)\sin^{3}(2y)dy
derivative of 1/9 x-ln(3x)	\frac{d}{dx}(\frac{1}{9}x-\ln(3x))
derivative of 6sqrt(x)+3\sqrt[3]{x}	derivative\:6\sqrt{x}+3\sqrt[3]{x}
area y=x^2,y=sqrt(8x)	area\:y=x^{2},y=\sqrt{8x}
y^'-6x^2y=0,y(1)=e	y^{\prime\:}-6x^{2}y=0,y(1)=e
derivative of y=((x+4)(x^2-4x+16))/(x^3)	derivative\:y=\frac{(x+4)(x^{2}-4x+16)}{x^{3}}
limit as x approaches 2 of 2/(4x+3)	\lim\:_{x\to\:2}(\frac{2}{4x+3})
integral of 1/((x-5)^2)-1	\int\:\frac{1}{(x-5)^{2}}-1dx
derivative of 1/(2sqrt(x))	derivative\:\frac{1}{2\sqrt{x}}
integral of t^{-4}e^t	\int\:t^{-4}e^{t}dt
derivative of 7x^3+3x-12	\frac{d}{dx}(7x^{3}+3x-12)
derivative of x/(4x+3ln(x))	\frac{d}{dx}(\frac{x}{4x+3\ln(x)})
integral of (x^2)/(3+x)	\int\:\frac{x^{2}}{3+x}dx
(\partial)/(\partial x)(3xyz^2)	\frac{\partial\:}{\partial\:x}(3xyz^{2})
laplacetransform s+1	laplacetransform\:s+1
integral of (4x+1)^5	\int\:(4x+1)^{5}dx
derivative of sqrt(x+9)	derivative\:\sqrt{x+9}
integral from 0 to 3 of 2pix(3x)	\int\:_{0}^{3}2πx(3x)dx
(x^{2x})^'	(x^{2x})^{\prime\:}
integral of cos^7(4x)	\int\:\cos^{7}(4x)dx
(\partial)/(\partial x)(4x^4y)	\frac{\partial\:}{\partial\:x}(4x^{4}y)
integral of 2x*cos(x)	\int\:2x\cdot\:\cos(x)dx
slope ofintercept (3,6),(5,5)	slopeintercept\:(3,6),(5,5)
(d^2}{dx^2}(\frac{6x^5)/5-3x)	\frac{d^{2}}{dx^{2}}(\frac{6x^{5}}{5}-3x)
y^{''}-6y^'+10y=0,y(0)=3,y^'(0)=-2	y^{\prime\:\prime\:}-6y^{\prime\:}+10y=0,y(0)=3,y^{\prime\:}(0)=-2
tangent of 7x^2+4x-5	tangent\:7x^{2}+4x-5
derivative of \sqrt[3]{(x^2+1^2})	\frac{d}{dx}(\sqrt[3]{(x^{2}+1)^{2}})
integral of-5xcos(x)	\int\:-5x\cos(x)dx
derivative of (y-x^2)	\frac{d}{dx}((y-x)^{2})
limit as x approaches 2 of \|x-3\|	\lim\:_{x\to\:2}(\left\|x-3\right\|)
integral of cos(t)-sin(t)	\int\:\cos(t)-\sin(t)dt
f(x)=sqrt(x^3+x)	f(x)=\sqrt{x^{3}+x}
(dy)/(dx)(2x+y+1)=1	\frac{dy}{dx}(2x+y+1)=1
derivative of 3x^2+2yx	\frac{d}{dx}(3x^{2}+2yx)
area-4x^2+6.25x+8,2.5x+7,0	area\:-4x^{2}+6.25x+8,2.5x+7,0
area y=4,2sqrt(x),((-3x+7))/2	area\:y=4,2\sqrt{x},\frac{(-3x+7)}{2}
sum from n=1 to infinity of (1+k/n)^n	\sum\:_{n=1}^{\infty\:}(1+\frac{k}{n})^{n}
limit as x approaches-8-of (-5x+2)/(x+8)	\lim\:_{x\to\:-8-}(\frac{-5x+2}{x+8})
integral of 3xsin(3x)	\int\:3x\sin(3x)dx
integral of xsqrt(x^2-16)	\int\:x\sqrt{x^{2}-16}dx
derivative of x^3-10x^2+36x	\frac{d}{dx}(x^{3}-10x^{2}+36x)
integral of 9xsqrt(y)	\int\:9x\sqrt{y}dy
derivative of \sqrt[3]{x}	derivative\:\sqrt[3]{x}
derivative of 1/(\sqrt[3]{(9x+1)^2)}	derivative\:\frac{1}{\sqrt[3]{(9x+1)^{2}}}
limit as x approaches infinity of x-4	\lim\:_{x\to\:\infty\:}(x-4)
derivative of-e^{cos(x}sin(x))	\frac{d}{dx}(-e^{\cos(x)}\sin(x))
derivative of y=3^{1-x}	derivative\:y=3^{1-x}
area sqrt(x), 1/x ,x=3	area\:\sqrt{x},\frac{1}{x},x=3
integral of sin(2x+pi/2)	\int\:\sin(2x+\frac{π}{2})dx
derivative of f(x)=3t-t^2	derivative\:f(x)=3t-t^{2}
derivative of (-6/((1+x)^4))	\frac{d}{dx}(\frac{-6}{(1+x)^{4}})
tangent of f(x)=(x^2+1)^{x+1},\at x=0	tangent\:f(x)=(x^{2}+1)^{x+1},\at\:x=0
derivative of cos((1-e^{9x}/(1+e^{9x)}))	\frac{d}{dx}(\cos(\frac{1-e^{9x}}{1+e^{9x}}))
integral of 2x+5x^{-2}	\int\:2x+5x^{-2}dx
(d^2)/(dx^2)(17e^{x^2})	\frac{d^{2}}{dx^{2}}(17e^{x^{2}})
integral of (7x^3-7)^4x^2	\int\:(7x^{3}-7)^{4}x^{2}dx
derivative of sqrt(x^2-2x+3)	\frac{d}{dx}(\sqrt{x^{2}-2x+3})
derivative of \sqrt[3]{(x^2-4^2})	\frac{d}{dx}(\sqrt[3]{(x^{2}-4)^{2}})
limit as x approaches-1 of x/(5sin(x+1))	\lim\:_{x\to\:-1}(\frac{x}{5\sin(x+1)})
implicit (dy)/(dx),x-y=xy	implicit\:\frac{dy}{dx},x-y=xy
integral of (x^2+2)/(sqrt(x))	\int\:\frac{x^{2}+2}{\sqrt{x}}dx
limit as x approaches 2 of sqrt(x+5)	\lim\:_{x\to\:2}(\sqrt{x+5})
integral from 0 to 1 of 1/(x^{18/19)}	\int\:_{0}^{1}\frac{1}{x^{\frac{18}{19}}}dx
limit as x approaches pi/4 of (1-2sin(2x))/(cos(x)-sin(x))	\lim\:_{x\to\:\frac{π}{4}}(\frac{1-2\sin(2x)}{\cos(x)-\sin(x)})
derivative of 3x^2-5x+7	\frac{d}{dx}(3x^{2}-5x+7)
integral of cos(1+x)	\int\:\cos(1+x)dx
y^{''}+25y=cos(8t)	y^{\prime\:\prime\:}+25y=\cos(8t)
derivative of sqrt((3x^{-2)+2/(x^2+8)})	\frac{d}{dx}(\sqrt{\frac{3x^{-2}+2}{x^{2}+8}})
derivative of-(-2ln(x+3)/(x^3))	\frac{d}{dx}(-\frac{-2\ln(x)+3}{x^{3}})
inverse oflaplace ((12s+3))/(s^2(2s+8))	inverselaplace\:\frac{(12s+3)}{s^{2}(2s+8)}
integral of 1/(-x^{-2)+2x}	\int\:\frac{1}{-x^{-2}+2x}dx
y^'+y/(9.33)=6.429	y^{\prime\:}+\frac{y}{9.33}=6.429
y^{''}=x^4	y^{\prime\:\prime\:}=x^{4}
inverse oflaplace s/(s+3)	inverselaplace\:\frac{s}{s+3}
(dx)/(dt)=(x^2+tsqrt(9t^2+x^2))/(tx)	\frac{dx}{dt}=\frac{x^{2}+t\sqrt{9t^{2}+x^{2}}}{tx}
taylor ((1+x))/(1-x)	taylor\:\frac{(1+x)}{1-x}
derivative of 3/4 x	\frac{d}{dx}(\frac{3}{4}x)
(\partial)/(\partial y)(x/z+y/z)	\frac{\partial\:}{\partial\:y}(\frac{x}{z}+\frac{y}{z})
inverse oflaplace s/((s+2))	inverselaplace\:\frac{s}{(s+2)}
y^'= y/x ,y(2)=2	y^{\prime\:}=\frac{y}{x},y(2)=2
integral of ((-3x^3+\sqrt[5]{x}))/(5x)	\int\:\frac{(-3x^{3}+\sqrt[5]{x})}{5x}dx
derivative of e^{-\|x\|}	\frac{d}{dx}(e^{-\left\|x\right\|})
limit as x approaches-2 of (x+2)/(2x+4)	\lim\:_{x\to\:-2}(\frac{x+2}{2x+4})
integral of 1/((x^2-1)^{3/2)}	\int\:\frac{1}{(x^{2}-1)^{\frac{3}{2}}}dx
area y=4x^2-1,y=1-4x^2	area\:y=4x^{2}-1,y=1-4x^{2}
y'=y(2-y)	y\prime\:=y(2-y)
limit as x approaches 0 of 2x-x^2	\lim\:_{x\to\:0}(2x-x^{2})
(\partial)/(\partial s)(s^2t)	\frac{\partial\:}{\partial\:s}(s^{2}t)
limit as x approaches-1 of arcsin(x)	\lim\:_{x\to\:-1}(\arcsin(x))
f(x)=5x(sin(x)+cos(x))	f(x)=5x(\sin(x)+\cos(x))
integral of 2sin^2(x)cos^2(x)	\int\:2\sin^{2}(x)\cos^{2}(x)dx
((x+5)e^{1/x})^'	((x+5)e^{\frac{1}{x}})^{\prime\:}
derivative of y=6x(2x+1)^2+(2x+1)^3	derivative\:y=6x(2x+1)^{2}+(2x+1)^{3}

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