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Popular Calculus Problems

derivative of arcsin(x/7)	\frac{d}{dx}(\arcsin(\frac{x}{7}))
(\partial)/(\partial x)(xe^{xy}-x/(y^2))	\frac{\partial\:}{\partial\:x}(xe^{xy}-\frac{x}{y^{2}})
tangent of ((8e^{(9x)}))/((5x-2))	tangent\:\frac{(8e^{(9x)})}{(5x-2)}
derivative of xe^{7x}	\frac{d}{dx}(xe^{7x})
integral of (sqrt(2x+1))	\int\:(\sqrt{2x+1})dx
derivative of 3x^2sin(4x)	\frac{d}{dx}(3x^{2}\sin(4x))
derivative of x^{-2cos(x})	\frac{d}{dx}(x^{-2\cos(x)})
limit as x approaches 0 of ((e^x-e^{-x}-2x))/(1-sin(x))	\lim\:_{x\to\:0}(\frac{(e^{x}-e^{-x}-2x)}{1-\sin(x)})
limit as x approaches infinity of x*pi	\lim\:_{x\to\:\infty\:}(x\cdot\:π)
limit as x approaches infinity of 1/6	\lim\:_{x\to\:\infty\:}(\frac{1}{6})
y^'=1+x^2	y^{\prime\:}=1+x^{2}
derivative of 3/((2x^{-2)})	\frac{d}{dx}(\frac{3}{(2x)^{-2}})
integral of (16x^2)/((x-6)(x+2)^2)	\int\:\frac{16x^{2}}{(x-6)(x+2)^{2}}dx
derivative of ((k^2x^3-6kx+9))/(x-1)	derivative\:\frac{(k^{2}x^{3}-6kx+9)}{x-1}
integral of x/(2x^2+12x+23)	\int\:\frac{x}{2x^{2}+12x+23}dx
x(x+y)y^'=y(x-y)	x(x+y)y^{\prime\:}=y(x-y)
integral of sin(u)cos(u)	\int\:\sin(u)\cos(u)du
f(x)=cos(sqrt(x))	f(x)=\cos(\sqrt{x})
integral of (e^{4x})/x	\int\:\frac{e^{4x}}{x}dx
integral of 2(2x+6)^5	\int\:2(2x+6)^{5}dx
integral of (2x+1)/(sqrt(x+4))	\int\:\frac{2x+1}{\sqrt{x+4}}dx
integral of (12)/(x^3+2x^2-3x)	\int\:\frac{12}{x^{3}+2x^{2}-3x}dx
y^{''}-y^'-4y=0	y^{\prime\:\prime\:}-y^{\prime\:}-4y=0
derivative of e^{(x})	\frac{d}{dx}(e^{(x)})
limit as x approaches infinity of 1/x+x	\lim\:_{x\to\:\infty\:}(\frac{1}{x}+x)
derivative of 4e^t	derivative\:4e^{t}
limit as x approaches 4 of 2/((x+4)^3)	\lim\:_{x\to\:4}(\frac{2}{(x+4)^{3}})
laplacetransform 3e^{-2t}cos(t)	laplacetransform\:3e^{-2t}\cos(t)
derivative of sqrt(t^2+1)	derivative\:\sqrt{t^{2}+1}
derivative of 5+3sqrt(x)	\frac{d}{dx}(5+3\sqrt{x})
integral of (5x-3)/(x^2+4)	\int\:\frac{5x-3}{x^{2}+4}dx
integral of 1/(x^2+4x+13)	\int\:\frac{1}{x^{2}+4x+13}dx
limit as x approaches pi of ln\|cos(x)-7\|	\lim\:_{x\to\:π}(\ln\left\|\cos(x)-7\right\|)
integral from 0 to pi/2 of cos^7(x)	\int\:_{0}^{\frac{π}{2}}\cos^{7}(x)dx
6y^{''}+10y^'=0	6y^{\prime\:\prime\:}+10y^{\prime\:}=0
(dy)/(dt)	\frac{dy}{dt}
sum from n=5 to infinity of 0.9^{2(n+1)}	\sum\:_{n=5}^{\infty\:}0.9^{2(n+1)}
integral of (54)/(x^2-81)	\int\:\frac{54}{x^{2}-81}dx
integral of x^3ln(2x)	\int\:x^{3}\ln(2x)dx
derivative of (3x+1/(x-1))	\frac{d}{dx}(\frac{3x+1}{x-1})
(\partial)/(\partial x)(e^xsin(x))	\frac{\partial\:}{\partial\:x}(e^{x}\sin(x))
limit as n approaches infinity of (n^2+3)/(n^3sqrt(n)+n^{5/2)}	\lim\:_{n\to\:\infty\:}(\frac{n^{2}+3}{n^{3}\sqrt{n}+n^{\frac{5}{2}}})
integral of (x^3+3x-2)/(x^2-x)	\int\:\frac{x^{3}+3x-2}{x^{2}-x}dx
derivative of 7/(x^7)	\frac{d}{dx}(\frac{7}{x^{7}})
integral from 1 to 8 of x^{-8/3}	\int\:_{1}^{8}x^{-\frac{8}{3}}dx
area y=x^2+9,y=10+2x	area\:y=x^{2}+9,y=10+2x
limit as x approaches 3 of sqrt(x^2-9)	\lim\:_{x\to\:3}(\sqrt{x^{2}-9})
integral of 3cos(t)-2sin(t)	\int\:3\cos(t)-2\sin(t)dt
laplacetransform e^{4t}(t^2+3t+5)	laplacetransform\:e^{4t}(t^{2}+3t+5)
integral of (-9x^2sec(3x^3+1))	\int\:(-9x^{2}\sec(3x^{3}+1))dx
derivative of (4x^{5x})	\frac{d}{dx}((4x)^{5x})
integral of (3x)^2+sqrt(2)	\int\:(3x)^{2}+\sqrt{2}dx
limit as x approaches 1 of 1-sqrt(2-x)	\lim\:_{x\to\:1}(1-\sqrt{2-x})
derivative of arccos(x^3)	\frac{d}{dx}(\arccos(x^{3}))
derivative of 2*x^2	\frac{d}{dx}(2\cdot\:x^{2})
inverse oflaplace ((s-2))/((s-3)(s+1))	inverselaplace\:\frac{(s-2)}{(s-3)(s+1)}
integral of (sin^7(4x))/(cos^4(4x))	\int\:\frac{\sin^{7}(4x)}{\cos^{4}(4x)}dx
limit as x approaches 0 of (sin(11x))/x	\lim\:_{x\to\:0}(\frac{\sin(11x)}{x})
derivative of (arcsin(x))^{e^{-x}}	derivative\:(\arcsin(x))^{e^{-x}}
derivative of log_{5}(sin(x))	derivative\:\log_{5}(\sin(x))
integral from 1/5 to 3 of 4xln(5x)	\int\:_{\frac{1}{5}}^{3}4x\ln(5x)dx
sum from n=1 to infinity of 7/(10^n)	\sum\:_{n=1}^{\infty\:}\frac{7}{10^{n}}
tangent of f(x)=2x^3+36x^2+192x+8	tangent\:f(x)=2x^{3}+36x^{2}+192x+8
limit as x approaches 0+of (e^x)/(1-e^{-x)}	\lim\:_{x\to\:0+}(\frac{e^{x}}{1-e^{-x}})
derivative of 4e^{6x}	\frac{d}{dx}(4e^{6x})
derivative of f(x)=sin(3x+1)	derivative\:f(x)=\sin(3x+1)
derivative of (4x^{6x})	\frac{d}{dx}((4x)^{6x})
limit as x approaches pi of xcos((7x)/6)	\lim\:_{x\to\:π}(x\cos(\frac{7x}{6}))
derivative of x/(x+6)	derivative\:\frac{x}{x+6}
integral of-2/(sqrt(7-7x^2))	\int\:-\frac{2}{\sqrt{7-7x^{2}}}dx
derivative of 5x^3-3x^5	\frac{d}{dx}(5x^{3}-3x^{5})
limit as t approaches-2 of (t+4)^2	\lim\:_{t\to\:-2}((t+4)^{2})
limit as x approaches-1 of 5x^2	\lim\:_{x\to\:-1}(5x^{2})
xy+y^'=64x	xy+y^{\prime\:}=64x
25y^{''}+5y=0	25y^{\prime\:\prime\:}+5y=0
tangent of f(x)=x^2+x,\at x=1	tangent\:f(x)=x^{2}+x,\at\:x=1
integral of 7cos(x)-4/(sqrt(1-x^2))	\int\:7\cos(x)-\frac{4}{\sqrt{1-x^{2}}}dx
laplacetransform sin(3t)e^{4t}	laplacetransform\:\sin(3t)e^{4t}
integral of sin(1/2)x	\int\:\sin(\frac{1}{2})xdx
area e^6,e^x,x=0	area\:e^{6},e^{x},x=0
limit as x approaches+2-of (\|x-x\|)/(x-2)	\lim\:_{x\to\:+2-}(\frac{\left\|x-x\right\|}{x-2})
(dy)/(dx)=(3x)/(3+x^2)	\frac{dy}{dx}=\frac{3x}{3+x^{2}}
y^'+x*e^{-x^{2/2}}=0	y^{\prime\:}+x\cdot\:e^{-x^{\frac{2}{2}}}=0
integral of (x-1)cos(x/3)	\int\:(x-1)\cos(\frac{x}{3})dx
derivative of x^{0.2}	\frac{d}{dx}(x^{0.2})
derivative of e^{6sin(7x)}	derivative\:e^{6\sin(7x)}
derivative of pi/3	\frac{d}{dx}(\frac{π}{3})
integral of 1/(sqrt(7+8x^2))	\int\:\frac{1}{\sqrt{7+8x^{2}}}dx
sum from n=0 to infinity of n!(x-4)^n	\sum\:_{n=0}^{\infty\:}n!(x-4)^{n}
derivative of arctan((2x/(1+x^2)))	\frac{d}{dx}(\arctan(\frac{2x}{1+x^{2}}))
d/(dt)(\sqrt[3]{t}+6sqrt(t^3))	\frac{d}{dt}(\sqrt[3]{t}+6\sqrt{t^{3}})
tangent of (x^2)/(x-1)	tangent\:\frac{x^{2}}{x-1}
derivative of f(x)= 1/(ln(x))	derivative\:f(x)=\frac{1}{\ln(x)}
derivative of (3-xe^x/(x+e^x))	\frac{d}{dx}(\frac{3-xe^{x}}{x+e^{x}})
derivative of cos(2xsin(3x))	\frac{d}{dx}(\cos(2x)\sin(3x))
integral of (7x^6-6/(x^6))	\int\:(7x^{6}-\frac{6}{x^{6}})dx
integral of x^2-3x+8	\int\:x^{2}-3x+8dx
slope ofintercept (-7,-6),(10,8)	slopeintercept\:(-7,-6),(10,8)
taylor (3x-10)^{4/3}	taylor\:(3x-10)^{\frac{4}{3}}
(\partial)/(\partial x)(1+x^4+y^4)	\frac{\partial\:}{\partial\:x}(1+x^{4}+y^{4})

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