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Popular Calculus Problems

(xydy)/(dx)=2x^2+2y^2	\frac{xydy}{dx}=2x^{2}+2y^{2}
integral of 5e^{x+5}	\int\:5e^{x+5}dx
2t*(dy)/(dt)+y=sqrt(t)	2t\cdot\:\frac{dy}{dt}+y=\sqrt{t}
integral from 1 to 3 of 2/(x^2+2x+1)	\int\:_{1}^{3}\frac{2}{x^{2}+2x+1}dx
tangent of f(x)=sqrt(x^2+5),\at x=-2	tangent\:f(x)=\sqrt{x^{2}+5},\at\:x=-2
area (16)/(4+x^2),y=1	area\:\frac{16}{4+x^{2}},y=1
area y= 1/(sqrt(4-9x^2)),(0, 1/3)	area\:y=\frac{1}{\sqrt{4-9x^{2}}},(0,\frac{1}{3})
derivative of-7sin(cos(x))	\frac{d}{dx}(-7\sin(\cos(x)))
(\partial)/(\partial x)((4x-4z)/(y+4z))	\frac{\partial\:}{\partial\:x}(\frac{4x-4z}{y+4z})
slope of (2x+2y)^3=8x^3+8y^3,(-1,1)	slope\:(2x+2y)^{3}=8x^{3}+8y^{3},(-1,1)
integral of (2x+1)(x-3)	\int\:(2x+1)(x-3)dx
(\partial)/(\partial x)(tan(xy^3))	\frac{\partial\:}{\partial\:x}(\tan(xy^{3}))
9y^{''}+6y^'+y=0,y(0)=1,y^'(0)=2	9y^{\prime\:\prime\:}+6y^{\prime\:}+y=0,y(0)=1,y^{\prime\:}(0)=2
derivative of (7x^2-11x)e^x	derivative\:(7x^{2}-11x)e^{x}
(\partial)/(\partial z)(z^2x+y^3)	\frac{\partial\:}{\partial\:z}(z^{2}x+y^{3})
derivative of x^5-e^xln(x)	\frac{d}{dx}(x^{5}-e^{x}\ln(x))
limit as x approaches-infinity of 5x	\lim\:_{x\to\:-\infty\:}(5x)
integral of 2cos(npix)	\int\:2\cos(nπx)dx
integral of sin(x)cos^3(x)	\int\:\sin(x)\cos^{3}(x)dx
integral of 1/(sqrt(5-4x^2))	\int\:\frac{1}{\sqrt{5-4x^{2}}}dx
integral from 0 to 2 of 2x-x^3	\int\:_{0}^{2}2x-x^{3}dx
integral of (x+5)/(sqrt(16-(x-4)^2))	\int\:\frac{x+5}{\sqrt{16-(x-4)^{2}}}dx
derivative of f(x)= 1/(sqrt(5x))	derivative\:f(x)=\frac{1}{\sqrt{5x}}
limit as x approaches 0+of 2x+8	\lim\:_{x\to\:0+}(2x+8)
derivative of tan({g}(x)(x))	\frac{d}{dx}(\tan({g}(x))(x))
limit as x approaches 4 of x^2+3x-1	\lim\:_{x\to\:4}(x^{2}+3x-1)
limit as x approaches 0 of \|0\|	\lim\:_{x\to\:0}(\left\|0\right\|)
(x^2e^{4x})^'	(x^{2}e^{4x})^{\prime\:}
limit as x approaches 0 of (x-3)/(2x-3)	\lim\:_{x\to\:0}(\frac{x-3}{2x-3})
(\partial)/(\partial z)(zsin(xy^2+2z))	\frac{\partial\:}{\partial\:z}(z\sin(xy^{2}+2z))
limit as x approaches 4 of 8x^2-9x+1	\lim\:_{x\to\:4}(8x^{2}-9x+1)
(\partial)/(\partial x)(y^{0.5}x)	\frac{\partial\:}{\partial\:x}(y^{0.5}x)
tangent of f(x)=x^3-4x^2,\at x=0	tangent\:f(x)=x^{3}-4x^{2},\at\:x=0
derivative of log_{e}(3)	\frac{d}{dx}(\log_{e}(3))
sum from n=2 to infinity of 1/(n(n+3))	\sum\:_{n=2}^{\infty\:}\frac{1}{n(n+3)}
(dy)/(dx)=(2x)/(y+x^2y)	\frac{dy}{dx}=\frac{2x}{y+x^{2}y}
derivative of ln((3+e^x)/(3-e^x))	derivative\:\ln(\frac{3+e^{x}}{3-e^{x}})
integral of (4-x^2)^2x^2	\int\:(4-x^{2})^{2}x^{2}dx
(\partial)/(\partial x)(2xy^3+cos(y))	\frac{\partial\:}{\partial\:x}(2xy^{3}+\cos(y))
(\partial)/(\partial x)(e^ye^x+ln(xy))	\frac{\partial\:}{\partial\:x}(e^{y}e^{x}+\ln(xy))
inverse oflaplace e^{sqrt(s^2+1)}	inverselaplace\:e^{\sqrt{s^{2}+1}}
(dy)/(dx)-1/x y=1-1/x	\frac{dy}{dx}-\frac{1}{x}y=1-\frac{1}{x}
derivative of f(x)=cos(6x)	derivative\:f(x)=\cos(6x)
derivative of (tan(3x))/(x^2)	derivative\:\frac{\tan(3x)}{x^{2}}
d/(dθ)(sin(θ)+2cos(θ))	\frac{d}{dθ}(\sin(θ)+2\cos(θ))
integral of (24x^6-24x^4+x)/x	\int\:\frac{24x^{6}-24x^{4}+x}{x}dx
integral from-sqrt(y) to sqrt(y of)\|x\|	\int\:_{-\sqrt{y}}^{\sqrt{y}}\left\|x\right\|dx
xdy=dx	xdy=dx
(\partial)/(\partial x)((6x)/(9+x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{6x}{9+x^{2}+y^{2}})
derivative of ln(sqrt((1+x/(1-x))))	\frac{d}{dx}(\ln(\sqrt{\frac{1+x}{1-x}}))
derivative of sin(3xy)	\frac{d}{dx}(\sin(3xy))
integral of x^25^{x^3}	\int\:x^{2}5^{x^{3}}dx
derivative of y=4sec(5x)	derivative\:y=4\sec(5x)
integral from 0 to 3 of 1/(1-x)	\int\:_{0}^{3}\frac{1}{1-x}dx
derivative of sqrt(sin(2x+1))	\frac{d}{dx}(\sqrt{\sin(2x+1)})
(\sqrt[4]{x})^'	(\sqrt[4]{x})^{\prime\:}
tangent of (10x)/(1+x^2)	tangent\:\frac{10x}{1+x^{2}}
integral from 2 to infinity of x^{-3}	\int\:_{2}^{\infty\:}x^{-3}dx
(\partial)/(\partial y)((6-x^2y^2)^2)	\frac{\partial\:}{\partial\:y}((6-x^{2}y^{2})^{2})
derivative of 8x^4tan(x)	\frac{d}{dx}(8x^{4}\tan(x))
f(x)= 2/(x^2)	f(x)=\frac{2}{x^{2}}
integral of 4/(9+4x)	\int\:\frac{4}{9+4x}dx
derivative of tan^5(sqrt(25xy^3+1))	\frac{d}{dx}(\tan^{5}(\sqrt{25xy^{3}+1}))
derivative of sinh(5x)	\frac{d}{dx}(\sinh(5x))
integral of ((2x+5))/(x^2+5x+6)	\int\:\frac{(2x+5)}{x^{2}+5x+6}dx
integral of (21x^2)/(sqrt(x^2-4))	\int\:\frac{21x^{2}}{\sqrt{x^{2}-4}}dx
derivative of (3x^5+8/(x^3))	\frac{d}{dx}(\frac{3x^{5}+8}{x^{3}})
sum from n=1 to infinity of n/(n^2+4)	\sum\:_{n=1}^{\infty\:}\frac{n}{n^{2}+4}
integral of sqrt(1-y)	\int\:\sqrt{1-y}dy
integral of 2xln(2x)	\int\:2x\ln(2x)dx
y^{''}-6y^'+10y=0	y^{\prime\:\prime\:}-6y^{\prime\:}+10y=0
derivative of C(x)=(4x+50)/(x+2)	derivative\:C(x)=\frac{4x+50}{x+2}
integral of xe^{sqrt(11)x+sqrt(3)}	\int\:xe^{\sqrt{11}x+\sqrt{3}}dx
integral of (x+3)(x^2+1)	\int\:(x+3)(x^{2}+1)dx
integral of 4arcsin(x)	\int\:4\arcsin(x)dx
limit as x approaches 1-of x^2-3	\lim\:_{x\to\:1-}(x^{2}-3)
derivative of 12.18+3.1sin(0.017x-1.376)	\frac{d}{dx}(12.18+3.1\sin(0.017x-1.376))
(dy)/(dx)=(x-4)e^{-2y},y(4)=ln(4)	\frac{dy}{dx}=(x-4)e^{-2y},y(4)=\ln(4)
derivative of ln(x^2y^3)	\frac{d}{dx}(\ln(x^{2}y^{3}))
integral of 2y^5	\int\:2y^{5}dy
sum from n=1 to infinity of sin(2n)	\sum\:_{n=1}^{\infty\:}\sin(2n)
integral of 1/(x(x^2-25)^{3/2)}	\int\:\frac{1}{x(x^{2}-25)^{\frac{3}{2}}}dx
derivative of y=2x^4sqrt(25-x^2)	derivative\:y=2x^{4}\sqrt{25-x^{2}}
(ln(1+x^2))^'	(\ln(1+x^{2}))^{\prime\:}
integral of (6/(x^3))	\int\:(\frac{6}{x^{3}})dx
(\partial)/(\partial y)(6xy^2-6x^2y+5xy)	\frac{\partial\:}{\partial\:y}(6xy^{2}-6x^{2}y+5xy)
tangent of x^4-5x^2+4	tangent\:x^{4}-5x^{2}+4
derivative of e^{sin(2x}+sin(e^{2x}))	\frac{d}{dx}(e^{\sin(2x)}+\sin(e^{2x}))
limit as x approaches 2 of 1/(x(x-2))	\lim\:_{x\to\:2}(\frac{1}{x(x-2)})
(\partial)/(\partial x)(x^2y+xy^3)	\frac{\partial\:}{\partial\:x}(x^{2}y+xy^{3})
limit as x approaches infinity of 2/3	\lim\:_{x\to\:\infty\:}(\frac{2}{3})
derivative of 1+x^{3/2}	\frac{d}{dx}(1+x^{\frac{3}{2}})
(\partial)/(\partial x)(7/(7x+8y))	\frac{\partial\:}{\partial\:x}(\frac{7}{7x+8y})
integral from-infinity to 6 of r*e^{r/3}	\int\:_{-\infty\:}^{6}r\cdot\:e^{\frac{r}{3}}dr
limit as x approaches 0+of sqrt(x)ln(2x)	\lim\:_{x\to\:0+}(\sqrt{x}\ln(2x))
implicit (dy)/(dx),y=5x^2	implicit\:\frac{dy}{dx},y=5x^{2}
derivative of f(x)=(cos(x)-4)/(2sin(x))	derivative\:f(x)=\frac{\cos(x)-4}{2\sin(x)}
simplify 1/3 t^3+7t^2+50t	simplify\:\frac{1}{3}t^{3}+7t^{2}+50t
derivative of (x^4+3x^2(1-5x))	\frac{d}{dx}((x^{4}+3x^{2})(1-5x))
(\partial)/(\partial y)(e^{2sqrt(x+y)})	\frac{\partial\:}{\partial\:y}(e^{2\sqrt{x+y}})

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