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Popular Calculus Problems

tangent of 3/(2sqrt(3x+13)),\at x=-3	tangent\:\frac{3}{2\sqrt{3x+13}},\at\:x=-3
solvefor x,(d^2x)/(dt^2)+x=(t^2+t)sin(t)	solvefor\:x,\frac{d^{2}x}{dt^{2}}+x=(t^{2}+t)\sin(t)
slope of (-5,11),(-10,6)	slope\:(-5,11),(-10,6)
derivative of pi/x	derivative\:\frac{π}{x}
y^'= y/(50+t)5,y(0)=30	y^{\prime\:}=\frac{y}{50+t}5,y(0)=30
integral of 16x^3e^{x^4+1}	\int\:16x^{3}e^{x^{4}+1}dx
integral of (ln(2x))/(x^2)	\int\:\frac{\ln(2x)}{x^{2}}dx
y^{1/2}((dy)/(dx))+y^{3/2}=1,y(0)=9	y^{\frac{1}{2}}(\frac{dy}{dx})+y^{\frac{3}{2}}=1,y(0)=9
limit as x approaches 0 of e^{-2/(x^3)}	\lim\:_{x\to\:0}(e^{-\frac{2}{x^{3}}})
derivative of f(x)=(x^3+7)e^x	derivative\:f(x)=(x^{3}+7)e^{x}
integral of (2x)/(x^2+14x+49)	\int\:\frac{2x}{x^{2}+14x+49}dx
sum from n=1 to infinity}\sqrt{5 of*2/n	\sum\:_{n=1}^{\infty\:}\sqrt{5}\cdot\:\frac{2}{n}
limit as x approaches 6 of (x^2-9x+18)/(x-6)	\lim\:_{x\to\:6}(\frac{x^{2}-9x+18}{x-6})
area y=6x,y= 3/2 x,y=7-x^2	area\:y=6x,y=\frac{3}{2}x,y=7-x^{2}
derivative of 2^{3^{4^x}}	\frac{d}{dx}(2^{3^{4^{x}}})
integral of e^{2x^2}x	\int\:e^{2x^{2}}xdx
integral of (kx)/(sqrt(1-x))	\int\:\frac{kx}{\sqrt{1-x}}dx
integral of e^{x^2+y^2}	\int\:e^{x^{2}+y^{2}}dx
integral of 8/(sqrt(1-x^2))	\int\:\frac{8}{\sqrt{1-x^{2}}}dx
integral of (x^2)/(sqrt(121+x^2))	\int\:\frac{x^{2}}{\sqrt{121+x^{2}}}dx
integral of (2-e^x)/(e^{9x)}	\int\:\frac{2-e^{x}}{e^{9x}}dx
integral from 0 to pi/2 of sec^4(t/2)	\int\:_{0}^{\frac{π}{2}}\sec^{4}(\frac{t}{2})dt
integral of ((5x^3-3\sqrt[5]{x})/(5x))	\int\:(\frac{5x^{3}-3\sqrt[5]{x}}{5x})dx
limit as x approaches 3 of (x-3)/(x^2-9)	\lim\:_{x\to\:3}(\frac{x-3}{x^{2}-9})
derivative of f(x)=((x+7)/(x+9))^6	derivative\:f(x)=(\frac{x+7}{x+9})^{6}
integral of 1/(4xsqrt(16x^2-25))	\int\:\frac{1}{4x\sqrt{16x^{2}-25}}dx
derivative of-3e^{-3x}+e^{4x}*4	derivative\:-3e^{-3x}+e^{4x}\cdot\:4
integral of y^2e^{3y}	\int\:y^{2}e^{3y}dy
sum from n=0 to infinity of 1/(n+7)	\sum\:_{n=0}^{\infty\:}\frac{1}{n+7}
integral from 0 to 9 of 8/((x-1)^{1/3)}	\int\:_{0}^{9}\frac{8}{(x-1)^{\frac{1}{3}}}dx
(\partial)/(\partial x)(9xcos(x)cos(y))	\frac{\partial\:}{\partial\:x}(9x\cdot\:\cos(x)\cdot\:\cos(y))
derivative of-2cos(x-x)	\frac{d}{dx}(-2\cos(x)-x)
integral of sin(a-x)	\int\:\sin(a-x)dx
limit as x approaches 2 of ((x+3))/(x+4)	\lim\:_{x\to\:2}(\frac{(x+3)}{x+4})
d/(dt)(tsin(pit))	\frac{d}{dt}(t\sin(πt))
integral of 1/(t^2)cos(1/t-1)	\int\:\frac{1}{t^{2}}\cos(\frac{1}{t}-1)dt
derivative of y= 4/(x^5)	derivative\:y=\frac{4}{x^{5}}
f(x)=2x^3ln(x)	f(x)=2x^{3}\ln(x)
integral of 1/(sqrt(a^2+v^2))	\int\:\frac{1}{\sqrt{a^{2}+v^{2}}}dv
derivative of 3/4 x^{4/3}	\frac{d}{dx}(\frac{3}{4}x^{\frac{4}{3}})
sum from n=1 to infinity of (6n)/(2n+1)	\sum\:_{n=1}^{\infty\:}\frac{6n}{2n+1}
inverse oflaplace e^{1-s}	inverselaplace\:e^{1-s}
derivative of ln(arctan(x+1))	derivative\:\ln(\arctan(x+1))
(\partial)/(\partial t)((rs)/(s^2+t^2))	\frac{\partial\:}{\partial\:t}(\frac{rs}{s^{2}+t^{2}})
derivative of (8x^2+3(3-x^2+7x))	\frac{d}{dx}((8x^{2}+3)(3-x^{2}+7x))
inverse oflaplace (e^{-s})/(s-2)	inverselaplace\:\frac{e^{-s}}{s-2}
derivative of 1/(x^2ln(x))	\frac{d}{dx}(\frac{1}{x^{2}\ln(x)})
tangent of f(x)=sqrt(7x+11),\at x=2	tangent\:f(x)=\sqrt{7x+11},\at\:x=2
(dy)/(dx)=(cos(8x))/(e^{8y)}	\frac{dy}{dx}=\frac{\cos(8x)}{e^{8y}}
derivative of g(x)=(5-x)^2(2x-1)^5	derivative\:g(x)=(5-x)^{2}(2x-1)^{5}
integral from-8 to 10 of x/2+10	\int\:_{-8}^{10}\frac{x}{2}+10dx
integral of (y^2)/4	\int\:\frac{y^{2}}{4}dy
laplacetransform t(sin(9t)+e^{-2t})	laplacetransform\:t(\sin(9t)+e^{-2t})
derivative of f(x)=sqrt(x)e^x	derivative\:f(x)=\sqrt{x}e^{x}
tangent of g(x)=x^2-8,\at x=-3	tangent\:g(x)=x^{2}-8,\at\:x=-3
derivative of 6x^2+9	\frac{d}{dx}(6x^{2}+9)
tangent of f(x)=((2x-1))/((x+5)),\at x=3	tangent\:f(x)=\frac{(2x-1)}{(x+5)},\at\:x=3
limit as x approaches 0 of (1+x)^{4/x}	\lim\:_{x\to\:0}((1+x)^{\frac{4}{x}})
x^2y^{''}+xy^'+4y=0	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}+4y=0
(\partial)/(\partial y)(3x^2+y)	\frac{\partial\:}{\partial\:y}(3x^{2}+y)
integral of (sec^3(x))	\int\:(\sec^{3}(x))dx
tangent of f(x)=x^2-5x+5,(0,5)	tangent\:f(x)=x^{2}-5x+5,(0,5)
d/(dt)(e^t(cos(t)))	\frac{d}{dt}(e^{t}(\cos(t)))
derivative of x(ln(x-1))	\frac{d}{dx}(x(\ln(x)-1))
integral from 0 to 3/4 of 1/(9+16x^2)	\int\:_{0}^{\frac{3}{4}}\frac{1}{9+16x^{2}}dx
derivative of 1/(sqrt(2pi)e^{-(x^2)/2})	\frac{d}{dx}(\frac{1}{\sqrt{2π}}e^{-\frac{x^{2}}{2}})
derivative of Ax^2e^x+Bxe^x+Ce^x	\frac{d}{dx}(Ax^{2}e^{x}+Bxe^{x}+Ce^{x})
sum from n=1 to infinity of ((n+1))/(n!)	\sum\:_{n=1}^{\infty\:}\frac{(n+1)}{n!}
integral of (y^3)/2	\int\:\frac{y^{3}}{2}dy
limit as t approaches infinity of (98)/(1+4e^{-0.1(t))}	\lim\:_{t\to\:\infty\:}(\frac{98}{1+4e^{-0.1(t)}})
integral of 1/(10x)	\int\:\frac{1}{10x}dx
derivative of y^2	derivative\:y^{2}
f^'(x)=3arctan(x^2-3x+2)	f^{\prime\:}(x)=3\arctan(x^{2}-3x+2)
integral of sqrt(1-4w^2)	\int\:\sqrt{1-4w^{2}}dw
integral of (sin(2x))/(cos^3(2x))	\int\:\frac{\sin(2x)}{\cos^{3}(2x)}dx
area x, 1/(x^2),1,3	area\:x,\frac{1}{x^{2}},1,3
(dy)/(dx)=-5yx,y(0)=50	\frac{dy}{dx}=-5yx,y(0)=50
derivative of x2^x	derivative\:x2^{x}
integral of sin^4(x)*cos^5(x)	\int\:\sin^{4}(x)\cdot\:\cos^{5}(x)dx
derivative of x(1+x^{-1})	\frac{d}{dx}(x(1+x)^{-1})
derivative of f(z)=(9z^4+3z^2+1)(3z^3-z)	derivative\:f(z)=(9z^{4}+3z^{2}+1)(3z^{3}-z)
integral of (4-2x)^2	\int\:(4-2x)^{2}dx
limit as x approaches-8 of 9x+10	\lim\:_{x\to\:-8}(9x+10)
y^{'''}-3y^{''}+3y^'-y=(e^x)/x	y^{\prime\:\prime\:\prime\:}-3y^{\prime\:\prime\:}+3y^{\prime\:}-y=\frac{e^{x}}{x}
integral of x^3+2x+3	\int\:x^{3}+2x+3dx
((dx))/((dy))=(8-(2x))/((100+2y))	\frac{(dx)}{(dy)}=\frac{8-(2x)}{(100+2y)}
derivative of (ln(x))/(3ln(x)+1)	derivative\:\frac{\ln(x)}{3\ln(x)+1}
derivative of-3x^{3/2}	derivative\:-3x^{\frac{3}{2}}
derivative of 6/((3-4x^5))	\frac{d}{dx}(\frac{6}{(3-4x)^{5}})
derivative of xy^2	derivative\:xy^{2}
limit as x approaches 2 of (sin(4x-8))/(3x-6)	\lim\:_{x\to\:2}(\frac{\sin(4x-8)}{3x-6})
derivative of ((e^x)/x)	\frac{d}{dx}(\frac{(e^{x})}{x})
derivative of f(x)=e^{xsqrt(7x+6)}	derivative\:f(x)=e^{x\sqrt{7x+6}}
inverse oflaplace 7/(2s^{2+8)}	inverselaplace\:\frac{7}{2s^{2+8}}
integral of cos^{2-2}(x)	\int\:\cos^{2-2}(x)dx
integral of (x^2+12x-1)/(x^3-x)	\int\:\frac{x^{2}+12x-1}{x^{3}-x}dx
integral of (-sin(x)tan(x))/1	\int\:\frac{-\sin(x)\tan(x)}{1}dx
derivative of (14/x)	\frac{d}{dx}(\frac{14}{x})
tangent of 6/(3x+1),\at x=-1	tangent\:\frac{6}{3x+1},\at\:x=-1
(\partial)/(\partial x)(-x-6)	\frac{\partial\:}{\partial\:x}(-x-6)

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