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Popular Calculus Problems

limit as x approaches-3+of (4x+3)/(x+3)	\lim\:_{x\to\:-3+}(\frac{4x+3}{x+3})
(dy)/(dx)=2xy^{1/2}	\frac{dy}{dx}=2xy^{\frac{1}{2}}
area 4-x^2,16-7x	area\:4-x^{2},16-7x
integral of (9-x)sqrt(x)	\int\:(9-x)\sqrt{x}dx
(\partial)/(\partial x)(x*e^{(-y)})	\frac{\partial\:}{\partial\:x}(x\cdot\:e^{(-y)})
tangent of x/(x-2)	tangent\:\frac{x}{x-2}
integral of cos(x)*sin(x)	\int\:\cos(x)\cdot\:\sin(x)dx
integral of xcos^4(x^2)	\int\:x\cos^{4}(x^{2})dx
y^{''}+4y^'+4y=3e^{-2t}	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=3e^{-2t}
x'(t)= 1/(3x^2+1),x(0)=1	x\prime\:(t)=\frac{1}{3x^{2}+1},x(0)=1
(\partial)/(\partial x)(e^{-6t}cos(pix))	\frac{\partial\:}{\partial\:x}(e^{-6t}\cos(πx))
(\partial)/(\partial y)(9ze^{xyz})	\frac{\partial\:}{\partial\:y}(9ze^{xyz})
integral from 0 to 1 of (e^{-0.1t})	\int\:_{0}^{1}(e^{-0.1t})dt
integral from 0 to pi of 2sin(nx)	\int\:_{0}^{π}2\sin(nx)dx
derivative of f(x)=sqrt(14x)	derivative\:f(x)=\sqrt{14x}
derivative of 2arctan(e^x)	\frac{d}{dx}(2\arctan(e^{x}))
derivative of 8(x+2^{3/2})	\frac{d}{dx}(8(x+2)^{\frac{3}{2}})
derivative of-2x^4+3x^3-x^2	\frac{d}{dx}(-2x^{4}+3x^{3}-x^{2})
implicit (dy)/(dx),40x^{1/3}y^{2/3}=480	implicit\:\frac{dy}{dx},40x^{\frac{1}{3}}y^{\frac{2}{3}}=480
integral of (2x)/((x-1)(x-2))	\int\:\frac{2x}{(x-1)(x-2)}dx
integral of ((x^2+3x+1))/x	\int\:\frac{(x^{2}+3x+1)}{x}dx
derivative of (4y^2-x^4/(4xy))	\frac{d}{dx}(\frac{4y^{2}-x^{4}}{4xy})
integral of (2x)/(x^2-49)	\int\:\frac{2x}{x^{2}-49}dx
taylor ln(3-x),2	taylor\:\ln(3-x),2
integral of (sec^2(sqrt(x)))/(sqrt(x))	\int\:\frac{\sec^{2}(\sqrt{x})}{\sqrt{x}}dx
integral of cos(npix)	\int\:\cos(nπx)dx
derivative of arccos((1-x^2/(1+x^2)))	\frac{d}{dx}(\arccos(\frac{1-x^{2}}{1+x^{2}}))
derivative of sqrt(x)(x-1)	derivative\:\sqrt{x}(x-1)
y^'=(x+1)^2	y^{\prime\:}=(x+1)^{2}
tangent of f(x)=3x^3-3x,(1,0)	tangent\:f(x)=3x^{3}-3x,(1,0)
integral of sin(2)(pix)cos(5)(pix)	\int\:\sin(2)(πx)\cos(5)(πx)dx
y^{''}-2y^'+1y=0	y^{\prime\:\prime\:}-2y^{\prime\:}+1y=0
integral of (sin^3(θ))/(cos^6(θ))	\int\:\frac{\sin^{3}(θ)}{\cos^{6}(θ)}dθ
integral of (sin(2x))/2	\int\:\frac{\sin(2x)}{2}dx
(\partial)/(\partial x)(x^zy^{1-z})	\frac{\partial\:}{\partial\:x}(x^{z}y^{1-z})
derivative of-3e^{x+4}+e^3	derivative\:-3e^{x+4}+e^{3}
tangent of f(x)=(x^2-18)(2x-3)	tangent\:f(x)=(x^{2}-18)(2x-3)
derivative of (-x^3/(y^3))	\frac{d}{dx}(\frac{-x^{3}}{y^{3}})
integral of te^{at}	\int\:te^{at}dt
sum from n=0 to infinity of 8/n-8/(n+1)	\sum\:_{n=0}^{\infty\:}\frac{8}{n}-\frac{8}{n+1}
5^'	5^{\prime\:}
integral of xe^{1/2 x^2}	\int\:xe^{\frac{1}{2}x^{2}}dx
integral of ((x+1)(x-1))/(x^2)	\int\:\frac{(x+1)(x-1)}{x^{2}}dx
derivative of log_{9}(ln(x))	derivative\:\log_{9}(\ln(x))
derivative of 1-4x	\frac{d}{dx}(1-4x)
limit as x approaches+0 of 8/(6+e^x)	\lim\:_{x\to\:+0}(\frac{8}{6+e^{x}})
integral from 1 to infinity of 3/(x^4)	\int\:_{1}^{\infty\:}\frac{3}{x^{4}}dx
derivative of ((17-x)sqrt(2x+8))/2	derivative\:\frac{(17-x)\sqrt{2x+8}}{2}
limit as x approaches-1 of x^4-2x^2-1	\lim\:_{x\to\:-1}(x^{4}-2x^{2}-1)
integral from 0 to 0.6 of (600x)	\int\:_{0}^{0.6}(600x)dx
(dy)/(dx)=((sec(y)))/((x-1)^2)	\frac{dy}{dx}=\frac{(\sec(y))}{(x-1)^{2}}
integral from 0 to pi of sin^5(x)	\int\:_{0}^{π}\sin^{5}(x)dx
integral of \sqrt[3]{x}+1/(\sqrt[3]{x)}	\int\:\sqrt[3]{x}+\frac{1}{\sqrt[3]{x}}dx
inverse oflaplace s/((s+1))	inverselaplace\:\frac{s}{(s+1)}
(\partial)/(\partial z)(x^{yz})	\frac{\partial\:}{\partial\:z}(x^{yz})
derivative of 11arccot(x+11arccot(1/x))	\frac{d}{dx}(11\arccot(x)+11\arccot(\frac{1}{x}))
derivative of (-5)/((2x^3+7)^2)	derivative\:\frac{-5}{(2x^{3}+7)^{2}}
slope of (2,7),(-5,2)	slope\:(2,7),(-5,2)
y^{''}-9y^'=0	y^{\prime\:\prime\:}-9y^{\prime\:}=0
integral of sin(2x)sqrt(1+cos^2(x))	\int\:\sin(2x)\sqrt{1+\cos^{2}(x)}dx
limit as x approaches 0 of (x^2-6x)/x	\lim\:_{x\to\:0}(\frac{x^{2}-6x}{x})
(\partial)/(\partial x)((4xy^2)/(x^2+y^4))	\frac{\partial\:}{\partial\:x}(\frac{4xy^{2}}{x^{2}+y^{4}})
(dy}{dx}=\frac{x^2-2y)/x	\frac{dy}{dx}=\frac{x^{2}-2y}{x}
limit as x approaches 2 of (2x+1)/(x-2)	\lim\:_{x\to\:2}(\frac{2x+1}{x-2})
derivative of sin(sqrt(3)x)	\frac{d}{dx}(\sin(\sqrt{3}x))
sum from n=1 to infinity of (2/3)^{n+2}	\sum\:_{n=1}^{\infty\:}(\frac{2}{3})^{n+2}
(\partial)/(\partial x)((-1)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{-1}{x^{2}+y^{2}})
laplacetransform e^{-3t}+3+2t+4t^2+5t^3	laplacetransform\:e^{-3t}+3+2t+4t^{2}+5t^{3}
derivative of sin(2x+cos(x))	\frac{d}{dx}(\sin(2x)+\cos(x))
integral of cos(x/(sqrt(2)))	\int\:\cos(\frac{x}{\sqrt{2}})dx
tangent of f(x)=5x-x^2,(1,4)	tangent\:f(x)=5x-x^{2},(1,4)
(1+x)dy-ydx=0	(1+x)dy-ydx=0
limit as x approaches infinity of 6^x	\lim\:_{x\to\:\infty\:}(6^{x})
limit as x approaches 0-of f(x)	\lim\:_{x\to\:0-}(f(x))
derivative of f(x)=-3e^{x+1}	derivative\:f(x)=-3e^{x+1}
tangent of f(x)=8x-x^2	tangent\:f(x)=8x-x^{2}
limit as x approaches 0+of 1/(x+1)	\lim\:_{x\to\:0+}(\frac{1}{x+1})
(\partial)/(\partial x)(1-x^2-y^2)	\frac{\partial\:}{\partial\:x}(1-x^{2}-y^{2})
limit as x approaches 1 of sqrt(x)-x	\lim\:_{x\to\:1}(\sqrt{x}-x)
(\partial)/(\partial x)(4x^{-1})	\frac{\partial\:}{\partial\:x}(4x^{-1})
tangent of f(x)=x^2+6x,\at a=3	tangent\:f(x)=x^{2}+6x,\at\:a=3
limit as x approaches 2 of sqrt(3x-2)	\lim\:_{x\to\:2}(\sqrt{3x-2})
derivative of (x^2)/(8+x)	derivative\:\frac{x^{2}}{8+x}
integral from 0 to 1 of 23cos(x^2)	\int\:_{0}^{1}23\cos(x^{2})dx
derivative of (tan(x)^{1/x})	\frac{d}{dx}((\tan(x))^{\frac{1}{x}})
integral of 1/(x^2+5x-6)	\int\:\frac{1}{x^{2}+5x-6}dx
derivative of 2cx	\frac{d}{dx}(2cx)
integral of 1/(x(ln(x^4))^9)	\int\:\frac{1}{x(\ln(x^{4}))^{9}}dx
e^xy(dy)/(dx)=e^{-y}+e^{-2x-y}	e^{x}y\frac{dy}{dx}=e^{-y}+e^{-2x-y}
laplacetransform 3sin(sqrt(2)t)	laplacetransform\:3\sin(\sqrt{2}t)
integral of-2x^{-4}	\int\:-2x^{-4}dx
derivative of cos(2x^3-3x)	\frac{d}{dx}(\cos(2x^{3}-3x))
derivative of f(x)=((5^{3x^7})/(8x^2))^4	derivative\:f(x)=(\frac{5^{3x^{7}}}{8x^{2}})^{4}
integral of (x-3)/(x^2-12x+36)	\int\:\frac{x-3}{x^{2}-12x+36}dx
sum from n=1 to infinity of n/(n+3)	\sum\:_{n=1}^{\infty\:}\frac{n}{n+3}
tangent of f(x)=(2+4x)(5-4x),\at x=1	tangent\:f(x)=(2+4x)(5-4x),\at\:x=1
tangent of y=2x^3-2x^2-2x	tangent\:y=2x^{3}-2x^{2}-2x
(dy)/(dx)+y/x =x^3	\frac{dy}{dx}+\frac{y}{x}=x^{3}
derivative of (e^{ax^2+bx+c}/x)	\frac{d}{dx}(\frac{e^{ax^{2}+bx+c}}{x})
limit as e approaches 1 of 5ln^2(e)	\lim\:_{e\to\:1}(5\ln^{2}(e))

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