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Popular Calculus Problems

d/(d{y)}({x}e^{({y})/({z)}})	\frac{d}{d{y}}({x}e^{\frac{{y}}{{z}}})
integral of ((arctan(x))^3)/(x^2+1)	\int\:\frac{(\arctan(x))^{3}}{x^{2}+1}dx
derivative of 2sin(2cos(x))	\frac{d}{dx}(2\sin(2\cos(x)))
derivative of 1/(sqrt(1+4x^2+x^4))	\frac{d}{dx}(\frac{1}{\sqrt{1+4x^{2}+x^{4}}})
integral of 2x^6-3x^5+11x^2+1	\int\:2x^{6}-3x^{5}+11x^{2}+1dx
integral of (-gt+V)	\int\:(-gt+V)dt
integral of e^{9x}cos(5x)	\int\:e^{9x}\cos(5x)dx
derivative of y=-x^3+2x	derivative\:y=-x^{3}+2x
maclaurin sin(pi/6+x)	maclaurin\:\sin(\frac{π}{6}+x)
derivative of 1-e^{-4x}	\frac{d}{dx}(1-e^{-4x})
integral of 1^{1/2}	\int\:1^{\frac{1}{2}}
expand (-x^2-4x)/((x^2-x-2)^2)	expand\:\frac{-x^{2}-4x}{(x^{2}-x-2)^{2}}
sum from n=1 to infinity of 4*0.3^n	\sum\:_{n=1}^{\infty\:}4\cdot\:0.3^{n}
(\partial)/(\partial x)(x^7yz^2+7yz)	\frac{\partial\:}{\partial\:x}(x^{7}yz^{2}+7yz)
area x=y,x=-y^2+6y	area\:x=y,x=-y^{2}+6y
derivative of sin(x)+1/7 cot(x)	derivative\:\sin(x)+\frac{1}{7}\cot(x)
integral from 50 to 80 of 25/3 x	\int\:_{50}^{80}\frac{25}{3}xdx
integral from 1 to 2 of (x^5+4x^7)/(x^4)	\int\:_{1}^{2}\frac{x^{5}+4x^{7}}{x^{4}}dx
(\partial)/(\partial x)(cos(xyz))	\frac{\partial\:}{\partial\:x}(\cos(xyz))
domain of f(x)=(3x+2)/(5x-1)	domain\:f(x)=\frac{3x+2}{5x-1}
derivative of (x^5+2)^2(x^4+4)^4	derivative\:(x^{5}+2)^{2}(x^{4}+4)^{4}
integral from 6 to 7 of x/(x^2-1)	\int\:_{6}^{7}\frac{x}{x^{2}-1}dx
(1+ln(x)+y/x)dx=(2-ln(x))dy	(1+\ln(x)+\frac{y}{x})dx=(2-\ln(x))dy
(\partial)/(\partial x)(e^{-3x-y})	\frac{\partial\:}{\partial\:x}(e^{-3x-y})
derivative of arccos((11/x))	\frac{d}{dx}(\arccos(\frac{11}{x}))
integral of (8e^{3t})/(1+e^{6t)}	\int\:\frac{8e^{3t}}{1+e^{6t}}dt
integral of x/(sqrt(x^2+5))	\int\:\frac{x}{\sqrt{x^{2}+5}}dx
derivative of y=(1-x/7)^{-7}	derivative\:y=(1-\frac{x}{7})^{-7}
integral of 1/(x^{1.1)}	\int\:\frac{1}{x^{1.1}}dx
limit as x approaches-2 of 3x^4+2x^2-x+4	\lim\:_{x\to\:-2}(3x^{4}+2x^{2}-x+4)
(\partial)/(\partial z)(e^x+z^2)	\frac{\partial\:}{\partial\:z}(e^{x}+z^{2})
area y=-588145x2+54170x-340.33,0,0.085	area\:y=-588145x2+54170x-340.33,0,0.085
integral of sin^5(10x)	\int\:\sin^{5}(10x)dx
d/(dθ)(3-3sin(θ))	\frac{d}{dθ}(3-3\sin(θ))
integral from 1 to 2 of (1/(x^2))	\int\:_{1}^{2}(\frac{1}{x^{2}})dx
integral of-1/(1+2x)	\int\:-\frac{1}{1+2x}dx
(\partial)/(\partial x)(e^{-y}sin(x))	\frac{\partial\:}{\partial\:x}(e^{-y}\sin(x))
(dy)/(dx)=(2x^3)/(y^2),y(2)=3	\frac{dy}{dx}=\frac{2x^{3}}{y^{2}},y(2)=3
derivative of sqrt(17-x^2-4y^2)	\frac{d}{dx}(\sqrt{17-x^{2}-4y^{2}})
integral of (sqrt(4-x^2))^3	\int\:(\sqrt{4-x^{2}})^{3}dx
derivative of ((4x^2+4x+4)/(sqrt(x)))	\frac{d}{dx}(\frac{(4x^{2}+4x+4)}{\sqrt{x}})
derivative of-1/((3+x)^2)	derivative\:-\frac{1}{(3+x)^{2}}
integral from 0 to 1/2 of-2arccos(x)	\int\:_{0}^{\frac{1}{2}}-2\arccos(x)dx
integral from 0 to infinity of 9e^{-9x}	\int\:_{0}^{\infty\:}9e^{-9x}dx
(\partial)/(\partial x)(1-3/y+x)	\frac{\partial\:}{\partial\:x}(1-\frac{3}{y}+x)
integral from 1 to 8 of sqrt(1+3x)	\int\:_{1}^{8}\sqrt{1+3x}dx
(dy)/(dx)=kae^{-kx}-by	\frac{dy}{dx}=kae^{-kx}-by
inverse oflaplace s/((s^2-1^2)^2)	inverselaplace\:\frac{s}{(s^{2}-1^{2})^{2}}
sum from n=1 to infinity of 1/(n^3-n)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{3}-n}
derivative of y=(3x)/(e^x)	derivative\:y=\frac{3x}{e^{x}}
taylor e^{-3x},2	taylor\:e^{-3x},2
integral of (3x+7)/((x+4)^2)	\int\:\frac{3x+7}{(x+4)^{2}}dx
derivative of x^{x^2}	derivative\:x^{x^{2}}
d/(dy)(xe^{xy})	\frac{d}{dy}(xe^{xy})
integral of (x^2-3x+6)	\int\:(x^{2}-3x+6)dx
integral of 2xcos^2(x)	\int\:2x\cos^{2}(x)dx
derivative of x^2-3x-4	\frac{d}{dx}(x^{2}-3x-4)
limit as x approaches 0+of e^{2/x}	\lim\:_{x\to\:0+}(e^{\frac{2}{x}})
integral of 2ysin(x)	\int\:2y\sin(x)dy
(dy)/(dx)=(1+x)(1+y)	\frac{dy}{dx}=(1+x)(1+y)
integral of (e^{-x}sin^2(x))/2	\int\:\frac{e^{-x}\sin^{2}(x)}{2}dx
limit as x approaches 0 of (sin(x))/(4x)	\lim\:_{x\to\:0}(\frac{\sin(x)}{4x})
derivative of Ae^{3x}+3Axe^{3x}	\frac{d}{dx}(Ae^{3x}+3Axe^{3x})
limit as x approaches 1 of 4x^5-2x^4-3	\lim\:_{x\to\:1}(4x^{5}-2x^{4}-3)
slope ofintercept (2,4),(-1,-5)	slopeintercept\:(2,4),(-1,-5)
-3y^'+(4y)/x =(y^4)/(x^2)	-3y^{\prime\:}+\frac{4y}{x}=\frac{y^{4}}{x^{2}}
(\partial)/(\partial x)(xcos(y-x))	\frac{\partial\:}{\partial\:x}(x\cos(y-x))
limit as x approaches 1 of sqrt((x-1))	\lim\:_{x\to\:1}(\sqrt{(x-1)})
integral from-3 to 0 of 1/(sqrt(9-x^2))	\int\:_{-3}^{0}\frac{1}{\sqrt{9-x^{2}}}dx
(\partial)/(\partial y)(e^{xy}sin(y))	\frac{\partial\:}{\partial\:y}(e^{xy}\sin(y))
integral from 0 to 20 of cos(pix)	\int\:_{0}^{20}\cos(πx)dx
integral of ln(x-5)	\int\:\ln(x-5)dx
derivative of (sin(x)^3)	\frac{d}{dx}((\sin(x))^{3})
limit as x approaches 0 of (x^2)/x	\lim\:_{x\to\:0}(\frac{x^{2}}{x})
tangent of f(x)=sqrt(x^2+9)	tangent\:f(x)=\sqrt{x^{2}+9}
derivative of x^2sin(pix)	\frac{d}{dx}(x^{2}\sin(πx))
(dy)/(dx)=ysec^2(x)	\frac{dy}{dx}=y\sec^{2}(x)
integral of 8xe^{0.5x^2}	\int\:8xe^{0.5x^{2}}dx
3y^{''}+108y=0	3y^{\prime\:\prime\:}+108y=0
(\partial)/(\partial x)((x-y)(xy-1))	\frac{\partial\:}{\partial\:x}((x-y)(xy-1))
derivative of (x*sin(x)/(1+cos(x)))	\frac{d}{dx}(\frac{x\cdot\:\sin(x)}{1+\cos(x)})
integral of (x-3)(sqrt(x+3))	\int\:(x-3)(\sqrt{x+3})dx
(dy}{dx}-\frac{1y)/x =1-1/x	\frac{dy}{dx}-\frac{1y}{x}=1-\frac{1}{x}
derivative of e^{-3x}-3e^{-3x}x	derivative\:e^{-3x}-3e^{-3x}x
integral of 12xln(7x)	\int\:12x\ln(7x)dx
derivative of (a^2+x^2e^{-x^2-a^2})	\frac{d}{dx}((a^{2}+x^{2})e^{-x^{2}-a^{2}})
derivative of-4cos^3(x)	\frac{d}{dx}(-4\cos^{3}(x))
tangent of y=x^2-2	tangent\:y=x^{2}-2
limit as x approaches 3 of 4	\lim\:_{x\to\:3}(4)
derivative of 15x-0.4x^2-80	derivative\:15x-0.4x^{2}-80
(\partial)/(\partial x)(cos(5x+9y+7z))	\frac{\partial\:}{\partial\:x}(\cos(5x+9y+7z))
integral of 1/(x^2-2x+4)	\int\:\frac{1}{x^{2}-2x+4}dx
derivative of f(x)=cos^6(x)	derivative\:f(x)=\cos^{6}(x)
(\partial)/(\partial x)(y/((1+x)^2))	\frac{\partial\:}{\partial\:x}(\frac{y}{(1+x)^{2}})
limit as x approaches-6 of-9x	\lim\:_{x\to\:-6}(-9x)
area e^{5x},e^{7x},x=1	area\:e^{5x},e^{7x},x=1
normal of y= 2/x ,(1,2)	normal\:y=\frac{2}{x},(1,2)
integral of 6x+sin(x)	\int\:6x+\sin(x)dx
(\partial)/(\partial y)(2y^2x-3)	\frac{\partial\:}{\partial\:y}(2y^{2}x-3)
integral of x(x+1)^3	\int\:x(x+1)^{3}dx

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