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Popular Calculus Problems

limit as x approaches 0+of (x^2)/6-4/x	\lim\:_{x\to\:0+}(\frac{x^{2}}{6}-\frac{4}{x})
(\partial)/(\partial y)(e^{2x}cos(2y))	\frac{\partial\:}{\partial\:y}(e^{2x}\cos(2y))
y^'=e^{x-2y}	y^{\prime\:}=e^{x-2y}
area x=-2,x=3,y=2x^2+6,y=0	area\:x=-2,x=3,y=2x^{2}+6,y=0
limit as x approaches 0+of (x^2+1)/x	\lim\:_{x\to\:0+}(\frac{x^{2}+1}{x})
limit as x approaches 2 of 1/(x^2-9)	\lim\:_{x\to\:2}(\frac{1}{x^{2}-9})
y^{''}+15y=0	y^{\prime\:\prime\:}+15y=0
derivative of {f}(x(x)^{{g}(x)})	\frac{d}{dx}({f}(x)(x)^{{g}(x)})
derivative of ((x+1(2x-5))/(2x+3))	\frac{d}{dx}(\frac{(x+1)(2x-5)}{2x+3})
(\partial)/(\partial y)(sin(3x+2y))	\frac{\partial\:}{\partial\:y}(\sin(3x+2y))
derivative of ye^y	derivative\:ye^{y}
integral of xcos(n)pix	\int\:x\cos(n)πxdx
integral of (x^2,left(sin(x)))	\int\:(x^{2},left(\sin(x)))dx
limit as z approaches-2 of (z^2-9)/(z-3)	\lim\:_{z\to\:-2}(\frac{z^{2}-9}{z-3})
integral of (6-x^2)^{3/2}	\int\:(6-x^{2})^{\frac{3}{2}}dx
sum from n=0 to infinity of 1/(2-e^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{2-e^{n}}
derivative of (x^2)/(x^2)	derivative\:\frac{x^{2}}{x^{2}}
integral of 2csc^2(x)	\int\:2\csc^{2}(x)dx
integral of sinh^{15}(x)	\int\:\sinh^{15}(x)dx
tangent of f(x)=x^2+4,\at x=3	tangent\:f(x)=x^{2}+4,\at\:x=3
integral of x(2x+3)^{99}	\int\:x(2x+3)^{99}dx
tangent of x^2-7x	tangent\:x^{2}-7x
integral from 0 to 8 of xsqrt(1+x)	\int\:_{0}^{8}x\sqrt{1+x}dx
derivative of 1/(6x-1)	derivative\:\frac{1}{6x-1}
integral of-6/pi x	\int\:-\frac{6}{π}xdx
limit as x approaches 0 of (3x)^{x^2}	\lim\:_{x\to\:0}((3x)^{x^{2}})
tangent of f(x)2x+10y-9=0	tangent\:f(x)2x+10y-9=0
integral of cos(-6x)	\int\:\cos(-6x)dx
derivative of y=(-13)/(\sqrt[4]{x)}	derivative\:y=\frac{-13}{\sqrt[4]{x}}
derivative of g(x)=x^2(1-3x)	derivative\:g(x)=x^{2}(1-3x)
integral of bx*sin((pix)/(2a))	\int\:bx\cdot\:\sin(\frac{πx}{2a})dx
(\partial)/(\partial y)(5x^2-2xy+3y^3)	\frac{\partial\:}{\partial\:y}(5x^{2}-2xy+3y^{3})
slope of (5.8)(3.9)	slope\:(5.8)(3.9)
y^{''}-y= 1/(e^x+e^{-x)}	y^{\prime\:\prime\:}-y=\frac{1}{e^{x}+e^{-x}}
(\partial)/(\partial x)(cos(xy))	\frac{\partial\:}{\partial\:x}(\cos(xy))
derivative of (tan(x)/(1+cos(x)))	\frac{d}{dx}(\frac{\tan(x)}{1+\cos(x)})
integral from 2 to 3 of (36)/(sqrt(3-x))	\int\:_{2}^{3}\frac{36}{\sqrt{3-x}}dx
sum from n=1 to infinity of 1/(3n)	\sum\:_{n=1}^{\infty\:}\frac{1}{3n}
limit as x approaches-5+of 8	\lim\:_{x\to\:-5+}(8)
tangent of 5x^3-4x^2+7x-8,\at x=1	tangent\:5x^{3}-4x^{2}+7x-8,\at\:x=1
integral from 0 to 1 of (4x+2)e^{2x}	\int\:_{0}^{1}(4x+2)e^{2x}dx
integral of 19tan^2(xse)c^3x	\int\:19\tan^{2}(xse)c^{3}xdx
derivative of f(x)=(3x)/(x^2-1)	derivative\:f(x)=\frac{3x}{x^{2}-1}
integral from 0 to 5 of pi((y^2)/3)^2	\int\:_{0}^{5}π(\frac{y^{2}}{3})^{2}dy
integral of (8x-12)(4x^2-12x)	\int\:(8x-12)(4x^{2}-12x)dx
derivative of 7sin(x)	derivative\:7\sin(x)
derivative of y=ln(sqrt((x+1)/(x-1)))	derivative\:y=\ln(\sqrt{\frac{x+1}{x-1}})
(dy)/(dt)=2ty^2+3y^2	\frac{dy}{dt}=2ty^{2}+3y^{2}
limit as x approaches+0+of (7x)^x	\lim\:_{x\to\:+0+}((7x)^{x})
integral from-infinity to infinity of xe^{x^2}	\int\:_{-\infty\:}^{\infty\:}xe^{x^{2}}dx
(dy)/(dx)=-k(y-a)	\frac{dy}{dx}=-k(y-a)
3yln(x)-xy^'=0	3y\ln(x)-xy^{\prime\:}=0
derivative of tan(x^2-4x^5)	\frac{d}{dx}(\tan(x^{2}-4x^{5}))
derivative of 2x^{1/2}+6x^{1/3}-2x^{3/2}	\frac{d}{dx}(2x^{\frac{1}{2}}+6x^{\frac{1}{3}}-2x^{\frac{3}{2}})
derivative of (sin(5x))/x	derivative\:\frac{\sin(5x)}{x}
(y+x)y^'=x-y	(y+x)y^{\prime\:}=x-y
(dy)/(dt)-2ty=-12t^2e^{t^2}	\frac{dy}{dt}-2ty=-12t^{2}e^{t^{2}}
integral of (x^4-x^2+2)/(x^2(x-1))	\int\:\frac{x^{4}-x^{2}+2}{x^{2}(x-1)}dx
integral of (Inx)/(x^2)	\int\:\frac{Inx}{x^{2}}dx
d/(dv)(sqrt(uv))	\frac{d}{dv}(\sqrt{uv})
derivative of \sqrt[3]{6x^2+1}	derivative\:\sqrt[3]{6x^{2}+1}
taylor 1/(x+1),0	taylor\:\frac{1}{x+1},0
integral from 0 to 5 of 2pi(7-x)(25-x^2)	\int\:_{0}^{5}2π(7-x)(25-x^{2})dx
integral of (arccos(x))/(sqrt(1-x^2))	\int\:\frac{\arccos(x)}{\sqrt{1-x^{2}}}dx
integral of-e^{2x}cos(2x)	\int\:-e^{2x}\cos(2x)dx
integral of ((1+e^{2x})^3)/(e^{-2x)}	\int\:\frac{(1+e^{2x})^{3}}{e^{-2x}}dx
derivative of y=3^x+1	derivative\:y=3^{x}+1
integral of (sin(x)-cos(2x))^2	\int\:(\sin(x)-\cos(2x))^{2}dx
integral of (7+7tan^2(θ))	\int\:(7+7\tan^{2}(θ))dθ
derivative of (x^4-3x^3-6x^2-3x+2/x)	\frac{d}{dx}(\frac{x^{4}-3x^{3}-6x^{2}-3x+2}{x})
tangent of f(x)= x/((2x-1)^6),\at x=1	tangent\:f(x)=\frac{x}{(2x-1)^{6}},\at\:x=1
(dy)/(dx)+3y+5=0	\frac{dy}{dx}+3y+5=0
laplacetransform cos(sqrt(2)x)	laplacetransform\:\cos(\sqrt{2}x)
derivative of 1/(7x+1)	\frac{d}{dx}(\frac{1}{7x+1})
derivative of (48)/(-4x)	derivative\:\frac{48}{-4x}
limit as x approaches 0+of x/(sqrt(x)-1)	\lim\:_{x\to\:0+}(\frac{x}{\sqrt{x}-1})
derivative of f(x)=(x-7)(5x+1)	derivative\:f(x)=(x-7)(5x+1)
derivative of e^{1/t}	derivative\:e^{\frac{1}{t}}
integral of x/(sqrt(x+6))	\int\:\frac{x}{\sqrt{x+6}}dx
derivative of e^x+2^{(-x}+2cos(x)-6)	\frac{d}{dx}(e^{x}+2^{(-x)}+2\cos(x)-6)
(dy)/(dx)+8y=e^xy^{-6}	\frac{dy}{dx}+8y=e^{x}y^{-6}
(2xdy)/(dx)+y=6x	\frac{2xdy}{dx}+y=6x
derivative of 4x^3-16x+5	\frac{d}{dx}(4x^{3}-16x+5)
integral of 1/(1+x^2+y^2)	\int\:\frac{1}{1+x^{2}+y^{2}}dy
y^{''}+16y=2sin(4t)	y^{\prime\:\prime\:}+16y=2\sin(4t)
limit as x approaches-3 of-2	\lim\:_{x\to\:-3}(-2)
limit as x approaches infinity of e^{1/x}sin(1/x)	\lim\:_{x\to\:\infty\:}(e^{\frac{1}{x}}\sin(\frac{1}{x}))
derivative of y=((x^2+2)/(x^2-2))^8	derivative\:y=(\frac{x^{2}+2}{x^{2}-2})^{8}
integral of cot(ax)	\int\:\cot(ax)dx
integral of csc^2(x)cot^5(x)	\int\:\csc^{2}(x)\cot^{5}(x)dx
integral of e^{1/50 x}	\int\:e^{\frac{1}{50}x}dx
(dy)/(dx)=-5yx	\frac{dy}{dx}=-5yx
integral from 0 to 4 of sqrt(1+x)	\int\:_{0}^{4}\sqrt{1+x}dx
integral of (-1)/(1-x)	\int\:\frac{-1}{1-x}dx
integral from 1 to 3 of (-x^2+4x-3)	\int\:_{1}^{3}(-x^{2}+4x-3)dx
limit as x approaches (0) of (ln(x))/x	\lim\:_{x\to\:(0)}(\frac{\ln(x)}{x})
limit as x approaches-3 of 2x-3ax+6a	\lim\:_{x\to\:-3}(2x-3ax+6a)
limit as x approaches 1+of (\|x-1\|)/(x-1)	\lim\:_{x\to\:1+}(\frac{\left\|x-1\right\|}{x-1})
(\partial)/(\partial x)((-x)/(y^2+x^2))	\frac{\partial\:}{\partial\:x}(\frac{-x}{y^{2}+x^{2}})
integral of ((x^3-4))/(x^3+2x^2+2x)	\int\:\frac{(x^{3}-4)}{x^{3}+2x^{2}+2x}dx

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