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Popular Calculus Problems

f^'(x)=sqrt(5x+1)	f^{\prime\:}(x)=\sqrt{5x+1}
(tan(y))^'	(\tan(y))^{\prime\:}
x^'=-3*x/(300)	x^{\prime\:}=-3\cdot\:\frac{x}{300}
integral from-2 to 8 of 6x^2+9	\int\:_{-2}^{8}6x^{2}+9dx
integral of (4x)/(2x^2-6)	\int\:\frac{4x}{2x^{2}-6}dx
x*(dy)/(dx)+y=(2y)/(1-y^2)	x\cdot\:\frac{dy}{dx}+y=\frac{2y}{1-y^{2}}
area y=x-3,y=sqrt(2x+2),y=-sqrt(2x+2)	area\:y=x-3,y=\sqrt{2x+2},y=-\sqrt{2x+2}
integral of (2/(sqrt(x)))	\int\:(\frac{2}{\sqrt{x}})dx
integral from 1 to infinity of 7/(x^3)	\int\:_{1}^{\infty\:}\frac{7}{x^{3}}dx
(\partial)/(\partial x)(1/(x-2))	\frac{\partial\:}{\partial\:x}(\frac{1}{x-2})
integral of x^3sqrt(x^4+6)	\int\:x^{3}\sqrt{x^{4}+6}dx
sum from n=2 to infinity of 2/(n^2-n)	\sum\:_{n=2}^{\infty\:}\frac{2}{n^{2}-n}
derivative of (a+b/({r(x)(x)^2})^3)	\frac{d}{dx}((a+\frac{b}{{r}(x)(x)^{2}})^{3})
integral from 0 to 2 of 1/(x^2+x-6)	\int\:_{0}^{2}\frac{1}{x^{2}+x-6}dx
limit as x approaches 11 of sqrt(10)	\lim\:_{x\to\:11}(\sqrt{10})
integral of (4sec^3(x))	\int\:(4\sec^{3}(x))dx
sum from n=-4 to infinity of ((-4)/9)^n	\sum\:_{n=-4}^{\infty\:}(\frac{-4}{9})^{n}
integral of 5^{sin(2x)}cos(2x)	\int\:5^{\sin(2x)}\cos(2x)dx
limit as x approaches 0 of 6x^3+7	\lim\:_{x\to\:0}(6x^{3}+7)
sum from n=1 to infinity of 1/n	\sum\:_{n=1}^{\infty\:}\frac{1}{n}
integral of 1+ye^{xy}	\int\:1+ye^{xy}dx
integral of-8(x-1)*(1-x)	\int\:-8(x-1)\cdot\:(1-x)dx
limit as h approaches-3 of (h^3+8)/(h+2)	\lim\:_{h\to\:-3}(\frac{h^{3}+8}{h+2})
(\partial)/(\partial x)(csc(x))	\frac{\partial\:}{\partial\:x}(\csc(x))
derivative of y=-3/(4x^4)+(24)/(5x^5)	derivative\:y=-\frac{3}{4x^{4}}+\frac{24}{5x^{5}}
derivative of (x+1)-1	derivative\:(x+1)-1
derivative of 1+3sin^2(x)	\frac{d}{dx}(1+3\sin^{2}(x))
integral of x^2sqrt(x^2-a^2)	\int\:x^{2}\sqrt{x^{2}-a^{2}}dx
integral from-infinity to-1 of e^{-8t}	\int\:_{-\infty\:}^{-1}e^{-8t}dt
area y=x^2-3x,x=0,x=7,y=4x	area\:y=x^{2}-3x,x=0,x=7,y=4x
(\partial)/(\partial y)(xy+yz+xz)	\frac{\partial\:}{\partial\:y}(xy+yz+xz)
limit as x approaches (pi/2)-of tan(x)	\lim\:_{x\to\:(\frac{π}{2})-}(\tan(x))
(\partial)/(\partial x)(x^my^n)	\frac{\partial\:}{\partial\:x}(x^{m}y^{n})
integral of x/(3+sqrt(x))	\int\:\frac{x}{3+\sqrt{x}}dx
tangent of (e^2)/(x^2-2x)	tangent\:\frac{e^{2}}{x^{2}-2x}
tangent of ((2))/(sin(x)+cos(x))	tangent\:\frac{(2)}{\sin(x)+\cos(x)}
derivative of (2x^2/(3y^2))	\frac{d}{dx}(\frac{2x^{2}}{3y^{2}})
derivative of 1-\sqrt[3]{x^2}	\frac{d}{dx}(1-\sqrt[3]{x^{2}})
limit as x approaches 0+of tan(x)*ln(x)	\lim\:_{x\to\:0+}(\tan(x)\cdot\:\ln(x))
integral of-x^{-1/2}	\int\:-x^{-\frac{1}{2}}dx
derivative of 8xsin(x-4pisin(x))	\frac{d}{dx}(8x\sin(x)-4π\sin(x))
derivative of ln^{-1}(x)	\frac{d}{dx}(\ln^{-1}(x))
limit as x approaches-7 of x+7	\lim\:_{x\to\:-7}(x+7)
x^2(d^2y)/(dx^2)+5x(dy)/(dx)-32y=0	x^{2}\frac{d^{2}y}{dx^{2}}+5x\frac{dy}{dx}-32y=0
limit as x approaches infinity of (3x+e^{-x})/(2x+e^{-2x)}	\lim\:_{x\to\:\infty\:}(\frac{3x+e^{-x}}{2x+e^{-2x}})
(\partial}{\partial x}((e^{\frac{x^2)/(4t)}tx)/2)	\frac{\partial\:}{\partial\:x}(\frac{e^{\frac{x^{2}}{4t}}tx}{2})
integral of 1/(x^2)sin(1/x)	\int\:\frac{1}{x^{2}}\sin(\frac{1}{x})dx
integral of 5xe^{x/5}	\int\:5xe^{\frac{x}{5}}dx
integral of (sec^2(x)+3)	\int\:(\sec^{2}(x)+3)dx
integral of ex	\int\:exdx
y^{''}+4y^'+4y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=0
derivative of (24/((1-x)^5))	\frac{d}{dx}(\frac{24}{(1-x)^{5}})
derivative of (ln\|x+2\|)^7	derivative\:(\ln\left\|x+2\right\|)^{7}
integral of (8x^3-4x^2-3x)/(6x)	\int\:\frac{8x^{3}-4x^{2}-3x}{6x}dx
derivative of (\sqrt[5]{x^2}+\sqrt[4]{x^5})/(2x)	derivative\:\frac{\sqrt[5]{x^{2}}+\sqrt[4]{x^{5}}}{2x}
(\partial ^2)/(\partial y\partial x)(xye^{-6y})	\frac{\partial\:^{2}}{\partial\:y\partial\:x}(xye^{-6y})
y^'-y=7	y^{\prime\:}-y=7
(\partial)/(\partial u)(sin(u))	\frac{\partial\:}{\partial\:u}(\sin(u))
derivative of f(x)=(c^5-x^5)/(c^5+c^5),c	derivative\:f(x)=\frac{c^{5}-x^{5}}{c^{5}+c^{5}},c
derivative of sqrt(3+5sin(s))	derivative\:\sqrt{3+5\sin(s)}
derivative of (x^2/(7+8x))	\frac{d}{dx}(\frac{x^{2}}{7+8x})
(\partial)/(\partial x)(1/(x^2+y^2+z^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{x^{2}+y^{2}+z^{2}})
limit as x approaches pi of tan(x/2)	\lim\:_{x\to\:π}(\tan(\frac{x}{2}))
limit as x approaches-4 of x^2-5	\lim\:_{x\to\:-4}(x^{2}-5)
integral of (x-1)/(x^2-3)	\int\:\frac{x-1}{x^{2}-3}dx
derivative of 1/(5x^2+3x)	derivative\:\frac{1}{5x^{2}+3x}
10y^{''}+1000y=130cos(8t)	10y^{\prime\:\prime\:}+1000y=130\cos(8t)
inverse oflaplace 3/((s-3)^3)	inverselaplace\:\frac{3}{(s-3)^{3}}
integral of e^{2x}(1-5e^{2x})^2	\int\:e^{2x}(1-5e^{2x})^{2}dx
(\partial)/(\partial x)(e^{-2x^2-3y^2})	\frac{\partial\:}{\partial\:x}(e^{-2x^{2}-3y^{2}})
integral of 9x^3(x^3+2x^2+x+8)	\int\:9x^{3}(x^{3}+2x^{2}+x+8)dx
limit as x approaches 4-of cx^2+7x	\lim\:_{x\to\:4-}(cx^{2}+7x)
integral of 1/2 (x-1/2 sin(2x))	\int\:\frac{1}{2}(x-\frac{1}{2}\sin(2x))dx
derivative of f(x)= 2/(3x^2)	derivative\:f(x)=\frac{2}{3x^{2}}
derivative of (4\sqrt[3]{x^2}/(x^2-8x))	\frac{d}{dx}(\frac{4\sqrt[3]{x^{2}}}{x^{2}-8x})
sum from n=1 to infinity of 2^{-2n}	\sum\:_{n=1}^{\infty\:}2^{-2n}
y^{''}+4y^'+4y=2x+6	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=2x+6
y^{''}-2y^'+2y=e^xsin(x)	y^{\prime\:\prime\:}-2y^{\prime\:}+2y=e^{x}\sin(x)
integral of 0.06*e^{t/(300)}	\int\:0.06\cdot\:e^{\frac{t}{300}}dt
derivative of ln((2x+1/(x-1)))	\frac{d}{dx}(\ln(\frac{2x+1}{x-1}))
sum from n=1 to infinity of 7/((n+1)!)	\sum\:_{n=1}^{\infty\:}\frac{7}{(n+1)!}
derivative of x^2sqrt(6x-7)	\frac{d}{dx}(x^{2}\sqrt{6x-7})
tangent of f(x)=1+5e^x,\at x=1	tangent\:f(x)=1+5e^{x},\at\:x=1
integral of (x+2)/(x^2(x-5))	\int\:\frac{x+2}{x^{2}(x-5)}dx
xy+y^2+x^2-x^2y^'=0	xy+y^{2}+x^{2}-x^{2}y^{\prime\:}=0
integral of sin(105x)sin(45x)	\int\:\sin(105x)\sin(45x)dx
(dy)/(dx)-2y=3x	\frac{dy}{dx}-2y=3x
(d^2)/(dx^2)(1/(x^8))	\frac{d^{2}}{dx^{2}}(\frac{1}{x^{8}})
derivative of ax^2e^x	\frac{d}{dx}(ax^{2}e^{x})
(\partial)/(\partial y)(3x^2-2y^2)	\frac{\partial\:}{\partial\:y}(3x^{2}-2y^{2})
limit as x approaches infinity of x/((ln(x))^x)	\lim\:_{x\to\:\infty\:}(\frac{x}{(\ln(x))^{x}})
(\partial)/(\partial x)(n^2x*(1-x)^n)	\frac{\partial\:}{\partial\:x}(n^{2}x\cdot\:(1-x)^{n})
integral of 1/((x^2+2x+2)^2)	\int\:\frac{1}{(x^{2}+2x+2)^{2}}dx
(dy)/(dt)+2y=1	\frac{dy}{dt}+2y=1
limit as x approaches 1-of 4x-6	\lim\:_{x\to\:1-}(4x-6)
y^'+y=3-e^t	y^{\prime\:}+y=3-e^{t}
integral of (x^3+x-1)/(x+3)	\int\:\frac{x^{3}+x-1}{x+3}dx
integral of csc^5(x)	\int\:\csc^{5}(x)dx
derivative of (4x)/((x^3-3)^2)	derivative\:\frac{4x}{(x^{3}-3)^{2}}
derivative of sqrt(x)+tan(x)	derivative\:\sqrt{x}+\tan(x)

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