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Popular Calculus Problems

derivative of y=ln(x+sqrt(x^2+6))	derivative\:y=\ln(x+\sqrt{x^{2}+6})
taylor x^{1/4},16	taylor\:x^{\frac{1}{4}},16
derivative of (ln(-2x^3+5x^2)/(-x))	\frac{d}{dx}(\frac{\ln(-2x^{3}+5x^{2})}{-x})
f(x)= 1/(1+x)	f(x)=\frac{1}{1+x}
limit as x approaches 1 of x^3-x+2	\lim\:_{x\to\:1}(x^{3}-x+2)
2y^{''}+y^'-4y=0	2y^{\prime\:\prime\:}+y^{\prime\:}-4y=0
integral of (cos(1/x))/x	\int\:\frac{\cos(\frac{1}{x})}{x}dx
integral of 4/3 pir^3	\int\:\frac{4}{3}πr^{3}dr
derivative of (x+1^3-x^3)	\frac{d}{dx}((x+1)^{3}-x^{3})
integral from 2 to 4 of 2/(x^2-6x+10)	\int\:_{2}^{4}\frac{2}{x^{2}-6x+10}dx
slope of (-2.1)(4.2)	slope\:(-2.1)(4.2)
tangent of f(x)=(x^2+7)(5-x),\at x=0	tangent\:f(x)=(x^{2}+7)(5-x),\at\:x=0
derivative of x^4+(y-2^3)	\frac{d}{dx}(x^{4}+(y-2)^{3})
integral of ((x^2-2x+1)^{1/5})/(1-x)	\int\:\frac{(x^{2}-2x+1)^{\frac{1}{5}}}{1-x}dx
integral of xsin^2(9x)	\int\:x\sin^{2}(9x)dx
2x^{3/2}	2x^{\frac{3}{2}}
integral of sin^3(5x)cos^{-2}(5x)	\int\:\sin^{3}(5x)\cos^{-2}(5x)dx
integral from 1 to 2 of (x^2+7)/(3x-x^2)	\int\:_{1}^{2}\frac{x^{2}+7}{3x-x^{2}}dx
inverse oflaplace s/((2s+1)((s+2)^2-1))	inverselaplace\:\frac{s}{(2s+1)((s+2)^{2}-1)}
tangent of f(x)=x^3-x,(-1,0)	tangent\:f(x)=x^{3}-x,(-1,0)
integral of 1/(sqrt(3x+8))	\int\:\frac{1}{\sqrt{3x+8}}dx
integral of sqrt(x^2+16)	\int\:\sqrt{x^{2}+16}dx
derivative of g(x)=((3x^2-2)/(2x+3))^3	derivative\:g(x)=(\frac{3x^{2}-2}{2x+3})^{3}
tangent of 5x^2-2x	tangent\:5x^{2}-2x
(e^y+1)^2e^{-y}dx+(e^x+1)^8e^{-x}dy=0	(e^{y}+1)^{2}e^{-y}dx+(e^{x}+1)^{8}e^{-x}dy=0
derivative of-a^2sin(ax)	\frac{d}{dx}(-a^{2}\sin(ax))
d/(dt)(e^{6t})	\frac{d}{dt}(e^{6t})
integral of x(5x^2+9)^8	\int\:x(5x^{2}+9)^{8}dx
derivative of y=e^{x^5}	derivative\:y=e^{x^{5}}
integral of sec(10w)tan(10w)	\int\:\sec(10w)\tan(10w)dw
limit as x approaches 0 of x/(x^2-2x)	\lim\:_{x\to\:0}(\frac{x}{x^{2}-2x})
derivative of (8x/(5-cot(x)))	\frac{d}{dx}(\frac{8x}{5-\cot(x)})
limit as x approaches 7 of 2x-\|x-7\|	\lim\:_{x\to\:7}(2x-\left\|x-7\right\|)
limit as x approaches 0 of e^{-6x}	\lim\:_{x\to\:0}(e^{-6x})
derivative of f(x)= 1/(y^2)	derivative\:f(x)=\frac{1}{y^{2}}
derivative of f(x)=(8x)/(1-x)	derivative\:f(x)=\frac{8x}{1-x}
integral of 1/(x^2sqrt(169-x^2))	\int\:\frac{1}{x^{2}\sqrt{169-x^{2}}}dx
integral of (ln(x))/(3x)	\int\:\frac{\ln(x)}{3x}dx
derivative of f(x)= x/(x^2+121)	derivative\:f(x)=\frac{x}{x^{2}+121}
derivative of x^3(3x+1)	\frac{d}{dx}(x^{3}(3x+1))
derivative of 1/(x^2-x-6)	\frac{d}{dx}(\frac{1}{x^{2}-x-6})
x(dy)/(dx)=y+xe^{y/x}	x\frac{dy}{dx}=y+xe^{\frac{y}{x}}
integral from 0 to pi/3 of sin^3(x)	\int\:_{0}^{\frac{π}{3}}\sin^{3}(x)dx
integral of (1-r)sqrt(r)	\int\:(1-r)\sqrt{r}dr
(\partial)/(\partial y)(-2x)	\frac{\partial\:}{\partial\:y}(-2x)
integral of e^{-x}*x	\int\:e^{-x}\cdot\:xdx
integral of 6^{sin(x)}cos(x)	\int\:6^{\sin(x)}\cos(x)dx
(d^2)/(dx^2)((x^2-5x)/(x+1))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}-5x}{x+1})
derivative of x^{-1}(x^2+1sqrt(x))	\frac{d}{dx}(x^{-1}(x^{2}+1)\sqrt{x})
2y^{''}-3y^'-14y=0	2y^{\prime\:\prime\:}-3y^{\prime\:}-14y=0
(dy)/(dx)=0.15y+200	\frac{dy}{dx}=0.15y+200
(-sqrt(x))^'	(-\sqrt{x})^{\prime\:}
derivative of ln(arcsin(x))	\frac{d}{dx}(\ln(\arcsin(x)))
integral of ((-x^2+x)/(x^4))	\int\:(\frac{-x^{2}+x}{x^{4}})dx
integral of 2x-2x^2	\int\:2x-2x^{2}dx
area f(x)=x^2,g(x)=2x	area\:f(x)=x^{2},g(x)=2x
integral of 3/(80-t)	\int\:\frac{3}{80-t}dt
(\partial)/(\partial x)((x^2-1)(y+2))	\frac{\partial\:}{\partial\:x}((x^{2}-1)(y+2))
integral from-2 to 1 of x^2+x-2	\int\:_{-2}^{1}x^{2}+x-2dx
integral of (2x(x^2+2)^2)	\int\:(2x(x^{2}+2)^{2})dx
derivative of tsin(t)+cos(t)	derivative\:t\sin(t)+\cos(t)
2t^2(dx)/(dt)=3tx+x^2	2t^{2}\frac{dx}{dt}=3tx+x^{2}
derivative of y= 5/(4x^3)	derivative\:y=\frac{5}{4x^{3}}
limit as x approaches 0-of x^2	\lim\:_{x\to\:0-}(x^{2})
(dN)/(dt)+N=Nte^{t+5}	\frac{dN}{dt}+N=Nte^{t+5}
limit as x approaches 0 of sqrt(x-3)	\lim\:_{x\to\:0}(\sqrt{x-3})
limit as t approaches 0 of 3t^2	\lim\:_{t\to\:0}(3t^{2})
derivative of 2(x-pi)	\frac{d}{dx}(2(x-π))
derivative of axe^x	\frac{d}{dx}(axe^{x})
(\partial)/(\partial u)(sqrt(5u^2+8v^2))	\frac{\partial\:}{\partial\:u}(\sqrt{5u^{2}+8v^{2}})
limit as x approaches 0 of (1-cos(x))/2	\lim\:_{x\to\:0}(\frac{1-\cos(x)}{2})
derivative of pi^5	\frac{d}{dx}(π^{5})
y^{''''}-5y^{''}+4y=0	y^{\prime\:\prime\:\prime\:\prime\:}-5y^{\prime\:\prime\:}+4y=0
sum from n=1 to infinity of arctan(11n)	\sum\:_{n=1}^{\infty\:}\arctan(11n)
derivative of-x(1+x^2^{-3/2})	\frac{d}{dx}(-x(1+x^{2})^{-\frac{3}{2}})
tangent of f(x)=x^2,(1,-3)	tangent\:f(x)=x^{2},(1,-3)
(\partial)/(\partial x)(x^2sin(kx))	\frac{\partial\:}{\partial\:x}(x^{2}\sin(kx))
derivative of e^x+e^{-2x}	\frac{d}{dx}(e^{x}+e^{-2x})
integral from 0 to pi of sqrt(sin(x))	\int\:_{0}^{π}\sqrt{\sin(x)}dx
y^{''}+y^'-2y=x^3-e^{-x}	y^{\prime\:\prime\:}+y^{\prime\:}-2y=x^{3}-e^{-x}
derivative of cos(x+ln(tan(x/2)))	\frac{d}{dx}(\cos(x)+\ln(\tan(\frac{x}{2})))
d/(d{y)}(ln(sqrt({x)^2+{y}^2+{z}^2}))	\frac{d}{d{y}}(\ln(\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}))
f(x)=sqrt(ln(2x+1))	f(x)=\sqrt{\ln(2x+1)}
tangent of (x^2)/(x-8)	tangent\:\frac{x^{2}}{x-8}
integral of x^2(x-8)^{13}	\int\:x^{2}(x-8)^{13}dx
(\partial)/(\partial x)(xye^{xy})	\frac{\partial\:}{\partial\:x}(xye^{xy})
derivative of ln(8-3x)	\frac{d}{dx}(\ln(8-3x))
derivative of (x^2-8x)^4	derivative\:(x^{2}-8x)^{4}
derivative of (e^xx-e^x/(x^2))	\frac{d}{dx}(\frac{e^{x}x-e^{x}}{x^{2}})
area y=2^x,y=4^x,y=4	area\:y=2^{x},y=4^{x},y=4
(\partial)/(\partial x)(sin(5x^4y-3xy^4))	\frac{\partial\:}{\partial\:x}(\sin(5x^{4}y-3xy^{4}))
(\partial)/(\partial y)((x^2+xy)^3)	\frac{\partial\:}{\partial\:y}((x^{2}+xy)^{3})
3y^'-2y=e^{-(pit)/2}	3y^{\prime\:}-2y=e^{-\frac{πt}{2}}
derivative of 6x^5e^x+e^xx^6	derivative\:6x^{5}e^{x}+e^{x}x^{6}
sum from n=1 to infinity of 4/(n(n+2))	\sum\:_{n=1}^{\infty\:}\frac{4}{n(n+2)}
derivative of x^{6/5}	derivative\:x^{\frac{6}{5}}
y^{''}-4y^'-5y=9e^{2t}	y^{\prime\:\prime\:}-4y^{\prime\:}-5y=9e^{2t}
integral of-picos(pi)x	\int\:-π\cos(π)xdx
(d^2)/(dx^2)(3x^2e^x)	\frac{d^{2}}{dx^{2}}(3x^{2}e^{x})
integral of sec(2)	\int\:\sec(2)

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