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Popular Calculus Problems

xy^'+y=6x^2,y(1)=2	xy^{\prime\:}+y=6x^{2},y(1)=2
limit as n approaches infinity of n^{10}	\lim\:_{n\to\:\infty\:}(n^{10})
derivative of f(x)=2x-xln\|x\|	derivative\:f(x)=2x-x\ln\left\|x\right\|
sum from n=0 to infinity of (1^n)/(2n+1)	\sum\:_{n=0}^{\infty\:}\frac{1^{n}}{2n+1}
derivative of x^8sin(x)	\frac{d}{dx}(x^{8}\sin(x))
(\partial}{\partial x}(\frac{x^4)/y)	\frac{\partial\:}{\partial\:x}(\frac{x^{4}}{y})
(\partial)/(\partial y)(6+xln(xy-5))	\frac{\partial\:}{\partial\:y}(6+x\ln(xy-5))
integral of 3sin^3(x)cos^7(x)	\int\:3\sin^{3}(x)\cos^{7}(x)dx
area x=16-y^2,x=y^2-16	area\:x=16-y^{2},x=y^{2}-16
sum from n=6 to infinity of (3n)/(12n)	\sum\:_{n=6}^{\infty\:}\frac{3n}{12n}
y^{'''}+y^'=2x^2	y^{\prime\:\prime\:\prime\:}+y^{\prime\:}=2x^{2}
derivative of f(x)=e^{tan(x)}	derivative\:f(x)=e^{\tan(x)}
(\partial)/(\partial u)(v/(1+uvw))	\frac{\partial\:}{\partial\:u}(\frac{v}{1+uvw})
integral of 1/(x(\sqrt[8]{x))}	\int\:\frac{1}{x(\sqrt[8]{x})}dx
derivative of g(t)=-4t^2+3t-3	derivative\:g(t)=-4t^{2}+3t-3
y^{''}+3y^'+2y=e^{-t}	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=e^{-t}
integral from-1 to 4 of (x^2+x^3)	\int\:_{-1}^{4}(x^{2}+x^{3})dx
laplacetransform x^3	laplacetransform\:x^{3}
derivative of f(x)=(1-3(a-1))/8	derivative\:f(x)=\frac{1-3(a-1)}{8}
derivative of (2x/(sqrt(4x^2+1)))	\frac{d}{dx}(\frac{2x}{\sqrt{4x^{2}+1}})
integral of (cos(x))/(1+cos(x))	\int\:\frac{\cos(x)}{1+\cos(x)}dx
(dy)/(dx)=(1-x^2)/(y^2)	\frac{dy}{dx}=\frac{1-x^{2}}{y^{2}}
derivative of sqrt(t+t^3)	derivative\:\sqrt{t+t^{3}}
(dy)/(dx)=8-4y	\frac{dy}{dx}=8-4y
integral of (e^{2sqrt(x)})/(3sqrt(x))	\int\:\frac{e^{2\sqrt{x}}}{3\sqrt{x}}dx
derivative of x^3-4x+7	\frac{d}{dx}(x^{3}-4x+7)
limit as x approaches 1 of x^2+x-2	\lim\:_{x\to\:1}(x^{2}+x-2)
d/(d{x)}(sqrt({x)^2+{y}^2+{z}^2})	\frac{d}{d{x}}(\sqrt{{x}^{2}+{y}^{2}+{z}^{2}})
derivative of 5/(\sqrt[4]{(x^3+2)^3)}	derivative\:\frac{5}{\sqrt[4]{(x^{3}+2)^{3}}}
limit as x approaches 4 of sqrt(16)	\lim\:_{x\to\:4}(\sqrt{16})
derivative of (2x-1/(x+1))	\frac{d}{dx}(\frac{2x-1}{x+1})
limit as x approaches infinity of x^7	\lim\:_{x\to\:\infty\:}(x^{7})
integral of cos(30)	\int\:\cos(30)dx
integral of f(x)	\int\:f(x)dx
y^'=(3xsec(y/x)+y)/x	y^{\prime\:}=\frac{3x\sec(\frac{y}{x})+y}{x}
derivative of f(x)=1-x	derivative\:f(x)=1-x
derivative of (x^2-2x/(x+1))	\frac{d}{dx}(\frac{x^{2}-2x}{x+1})
y^'=-y/x+e^x	y^{\prime\:}=-\frac{y}{x}+e^{x}
derivative of f(x)=sin(3x)-cos(2x)	derivative\:f(x)=\sin(3x)-\cos(2x)
(\partial)/(\partial x)(x^3+4)	\frac{\partial\:}{\partial\:x}(x^{3}+4)
integral from 0 to 1 of e^{-st}t	\int\:_{0}^{1}e^{-st}tdt
y^'=-2xtan(y)	y^{\prime\:}=-2x\tan(y)
slope of (5,-2),(7,10)	slope\:(5,-2),(7,10)
area y=3x,x=8-y^2	area\:y=3x,x=8-y^{2}
derivative of 15	\frac{d}{dx}(15)
integral of (2cos(x)-3sin(x)+x)	\int\:(2\cos(x)-3\sin(x)+x)dx
derivative of f(x)=(6x+7)(7x-8)	derivative\:f(x)=(6x+7)(7x-8)
integral of 10sin(5x)	\int\:10\sin(5x)dx
integral of (1+2x^2)^2	\int\:(1+2x^{2})^{2}dx
(dy)/(dx)=(2x)/(1+2y),y(2)=1	\frac{dy}{dx}=\frac{2x}{1+2y},y(2)=1
(2x)/y dx-(x^2)/(y^2)dy=0	\frac{2x}{y}dx-\frac{x^{2}}{y^{2}}dy=0
derivative of f(x)=(2x)/7+1	derivative\:f(x)=\frac{2x}{7}+1
integral of (3/(x^{3/4)}-4\sqrt[3]{x}+1)	\int\:(\frac{3}{x^{\frac{3}{4}}}-4\sqrt[3]{x}+1)dx
(dy)/(dx)=(x-2)e^{-2y}	\frac{dy}{dx}=(x-2)e^{-2y}
(\partial)/(\partial x)((2-x)(5-x-2y))	\frac{\partial\:}{\partial\:x}((2-x)(5-x-2y))
limit as x approaches 2 of (3x+4)/(5x+7)	\lim\:_{x\to\:2}(\frac{3x+4}{5x+7})
derivative of 1/(cos(x)+1/(sin(x+1)))	\frac{d}{dx}(\frac{1}{\cos(x)}+\frac{1}{\sin(x+1)})
d/(dθ)((e^{iθ}+e^{-iθ})/2)	\frac{d}{dθ}(\frac{e^{iθ}+e^{-iθ}}{2})
derivative of y=(t-sqrt(t))/(t^{1/3)}	derivative\:y=\frac{t-\sqrt{t}}{t^{\frac{1}{3}}}
integral of (4x+5)/(x^2+1)	\int\:\frac{4x+5}{x^{2}+1}dx
derivative of x^2*e^{4x}	\frac{d}{dx}(x^{2}\cdot\:e^{4x})
integral of 3sqrt(x)-6x	\int\:3\sqrt{x}-6xdx
(d^2)/(dx^2)((x^2+3)^7)	\frac{d^{2}}{dx^{2}}((x^{2}+3)^{7})
integral from 0 to 5.5 of 120x	\int\:_{0}^{5.5}120xdx
integral of (9x^2)	\int\:(9x^{2})dx
derivative of x^2sin(2x)	derivative\:x^{2}\sin(2x)
limit as x approaches 7 of sin((pix)/2)	\lim\:_{x\to\:7}(\sin(\frac{πx}{2}))
derivative of x-6	derivative\:x-6
integral of (sin(4x))/(cos(2x))	\int\:\frac{\sin(4x)}{\cos(2x)}dx
area y=-x^2+4x,y=x^2-2x	area\:y=-x^{2}+4x,y=x^{2}-2x
limit as x approaches+0+of arctan(x)	\lim\:_{x\to\:+0+}(\arctan(x))
tangent of x^4-5x^3+2	tangent\:x^{4}-5x^{3}+2
(\partial)/(\partial x)(x^2y^3)	\frac{\partial\:}{\partial\:x}(x^{2}y^{3})
slope of (4,-2),(1,1)	slope\:(4,-2),(1,1)
integral of (1+x^2)2x	\int\:(1+x^{2})2xdx
integral of 1/(x^2sqrt(16+9x^2))	\int\:\frac{1}{x^{2}\sqrt{16+9x^{2}}}dx
y^{''}-6y=9t	y^{\prime\:\prime\:}-6y=9t
integral of 5x^2+9	\int\:5x^{2}+9dx
tv^'(1-t^2)+2v=0	tv^{\prime\:}(1-t^{2})+2v=0
integral of x(x^2-1)^2	\int\:x(x^{2}-1)^{2}dx
taylor (1+x)^n	taylor\:(1+x)^{n}
derivative of f(x)=-(12)/((x-6)^2)	derivative\:f(x)=-\frac{12}{(x-6)^{2}}
integral of (5x^3+3x)/(x-1)	\int\:\frac{5x^{3}+3x}{x-1}dx
integral of (x^5+1)	\int\:(x^{5}+1)dx
y^{''}+8y^'-9y=e^{3x}	y^{\prime\:\prime\:}+8y^{\prime\:}-9y=e^{3x}
derivative of x(x-21^2)	\frac{d}{dx}(x(x-21)^{2})
inverse oflaplace ((e^{-2s}))/(s+1)	inverselaplace\:\frac{(e^{-2s})}{s+1}
derivative of 3sqrt(x-2)	\frac{d}{dx}(3\sqrt{x-2})
(\partial)/(\partial x)(2y-2)	\frac{\partial\:}{\partial\:x}(2y-2)
(\partial)/(\partial x)(x^6+xy^5+7)	\frac{\partial\:}{\partial\:x}(x^{6}+xy^{5}+7)
integral of (cos(x)+xcos(y)-y)	\int\:(\cos(x)+x\cos(y)-y)dy
(6+x)y^'=7y	(6+x)y^{\prime\:}=7y
integral of 3/(18+2t^2)	\int\:\frac{3}{18+2t^{2}}dt
derivative of cos(ti)	\frac{d}{dx}(\cos(t)i)
limit as x approaches 1 of 30	\lim\:_{x\to\:1}(30)
integral of 1/(5-6x)	\int\:\frac{1}{5-6x}dx
derivative of 2log_{3}(x)	\frac{d}{dx}(2\log_{3}(x))
integral from 0 to 2 of xsqrt(8-2x^2)	\int\:_{0}^{2}x\sqrt{8-2x^{2}}dx
integral of 2/(35sin(x)-12cos(x))	\int\:\frac{2}{35\sin(x)-12\cos(x)}dx
integral of xarctan(x^2)	\int\:x\arctan(x^{2})dx

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