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Popular Calculus Problems

derivative of 4x^3-24x^2+36x	\frac{d}{dx}(4x^{3}-24x^{2}+36x)
(dP)/(dt)=1P(500-P)	\frac{dP}{dt}=1P(500-P)
derivative of-sin(3x)	derivative\:-\sin(3x)
x*y^'+y= 1/(y^2)	x\cdot\:y^{\prime\:}+y=\frac{1}{y^{2}}
integral of 2xsqrt(1+4x^2)	\int\:2x\sqrt{1+4x^{2}}dx
derivative of cos(7^{6x})	\frac{d}{dx}(\cos(7^{6x}))
x^2(dy)/(dx)+xy=1	x^{2}\frac{dy}{dx}+xy=1
derivative of f(x)=9-4x^2	derivative\:f(x)=9-4x^{2}
integral of sec^2(6x)	\int\:\sec^{2}(6x)dx
integral of t/(e^t)	\int\:\frac{t}{e^{t}}dt
integral of (x+3)/(x^2-x+4)	\int\:\frac{x+3}{x^{2}-x+4}dx
y^{''}+2y^'+y=4e-t	y^{\prime\:\prime\:}+2y^{\prime\:}+y=4e-t
derivative of 1y^2-7y^4(y+9y^3)	derivative\:1y^{2}-7y^{4}(y+9y^{3})
limit as x approaches 36 of (x^2)/9-4/x	\lim\:_{x\to\:36}(\frac{x^{2}}{9}-\frac{4}{x})
integral of 7/(4+7x)	\int\:\frac{7}{4+7x}dx
(\partial)/(\partial x)(3x^2y+xsin(2y))	\frac{\partial\:}{\partial\:x}(3x^{2}y+x\sin(2y))
y^'=(3y^2-x^2)/(2xy)	y^{\prime\:}=\frac{3y^{2}-x^{2}}{2xy}
y^'+sin(t)y=-sin(t),y(0)=7	y^{\prime\:}+\sin(t)y=-\sin(t),y(0)=7
(\partial)/(\partial x)(1/4 x^ay^{1-a})	\frac{\partial\:}{\partial\:x}(\frac{1}{4}x^{a}y^{1-a})
integral of e^{-2}	\int\:e^{-2}dx
area 4x-12,[2,6]	area\:4x-12,[2,6]
integral of e^{2*x}	\int\:e^{2\cdot\:x}dx
derivative of (x^{12}-1)^3	derivative\:(x^{12}-1)^{3}
integral of (7x^3+x^2)/(sqrt(x))	\int\:\frac{7x^{3}+x^{2}}{\sqrt{x}}dx
limit as x approaches 2 of (7x-26)/(x-5)	\lim\:_{x\to\:2}(\frac{7x-26}{x-5})
limit as x approaches infinity of 3^x	\lim\:_{x\to\:\infty\:}(3^{x})
integral of 5sin^2(x)cos(x)	\int\:5\sin^{2}(x)\cos(x)dx
y^'=(y-y^2)/x	y^{\prime\:}=\frac{y-y^{2}}{x}
derivative of x^{2/5}	derivative\:x^{\frac{2}{5}}
tangent of sqrt(9-t)	tangent\:\sqrt{9-t}
(d^2)/(dx^2)((x^2-3x)/(x+1))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}-3x}{x+1})
sum from n=1 to infinity of 6e^{-5n}	\sum\:_{n=1}^{\infty\:}6e^{-5n}
integral of (12x^3-24x^2+5)/(x^2-2x)	\int\:\frac{12x^{3}-24x^{2}+5}{x^{2}-2x}dx
(\partial)/(\partial x)(sqrt(x)+4y)	\frac{\partial\:}{\partial\:x}(\sqrt{x}+4y)
integral of e^{2x}2x	\int\:e^{2x}2xdx
(\partial)/(\partial x)(sqrt(x^2-y))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}-y})
derivative of f(x)=x^3arcsin(x^2e^x)	derivative\:f(x)=x^{3}\arcsin(x^{2}e^{x})
inverse oflaplace (s-2)/(s^2+5s+6)	inverselaplace\:\frac{s-2}{s^{2}+5s+6}
derivative of (x^3)/4+1/(3x)	derivative\:\frac{x^{3}}{4}+\frac{1}{3x}
(\partial)/(\partial t)(3t)	\frac{\partial\:}{\partial\:t}(3t)
derivative of f(x)=sin(θ)cos(θ)	derivative\:f(x)=\sin(θ)\cos(θ)
(dv)/(dt)=-2v-32	\frac{dv}{dt}=-2v-32
y^{''}=-16y	y^{\prime\:\prime\:}=-16y
limit as x approaches 1 of e^{8x^2-8x}	\lim\:_{x\to\:1}(e^{8x^{2}-8x})
derivative of f(x)=(18e^x)/(7^x)	derivative\:f(x)=\frac{18e^{x}}{7^{x}}
derivative of f(x)=2.4x^2+13x	derivative\:f(x)=2.4x^{2}+13x
(\partial)/(\partial x)(sqrt(x^3y-y^4))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{3}y-y^{4}})
integral of tan^3(x)sec^8(x)	\int\:\tan^{3}(x)\sec^{8}(x)dx
derivative of 2/3 x^3	derivative\:\frac{2}{3}x^{3}
limit as x approaches 0+of tan(2/x)	\lim\:_{x\to\:0+}(\tan(\frac{2}{x}))
integral of e^{x^2+4x+3}(x+2)	\int\:e^{x^{2}+4x+3}(x+2)dx
(\partial)/(\partial x)(x^2z^2sin(4y))	\frac{\partial\:}{\partial\:x}(x^{2}z^{2}\sin(4y))
(\partial)/(\partial y)((xy)/((x-y)))	\frac{\partial\:}{\partial\:y}(\frac{xy}{(x-y)})
limit as x approaches 4 of (x^2-5)/(x+5)	\lim\:_{x\to\:4}(\frac{x^{2}-5}{x+5})
tangent of f(x)=3x^2-ln(x),(1,3)	tangent\:f(x)=3x^{2}-\ln(x),(1,3)
tangent of f(x)=x^5,\at x=4	tangent\:f(x)=x^{5},\at\:x=4
integral of (x^2+1)cos(2x)	\int\:(x^{2}+1)\cos(2x)dx
integral of sin(2x)e^{cos(2x)}	\int\:\sin(2x)e^{\cos(2x)}dx
integral of 7x^2+3+6/(x^2+1)	\int\:7x^{2}+3+\frac{6}{x^{2}+1}dx
derivative of (16/((5-x)^2)-1)	\frac{d}{dx}(\frac{16}{(5-x)^{2}}-1)
(pi/2)^'	(\frac{π}{2})^{\prime\:}
integral from 0 to 4 of 16-x^2	\int\:_{0}^{4}16-x^{2}dx
derivative of 3x^e+2e^x	derivative\:3x^{e}+2e^{x}
integral of (x+1)/(x(x-2)(x+3))	\int\:\frac{x+1}{x(x-2)(x+3)}dx
derivative of 6x(x^2-1)^2	derivative\:6x(x^{2}-1)^{2}
integral of x^30.2^{-x}x	\int\:x^{3}0.2^{-x}xdx
limit as x approaches+(-2) of 8/x	\lim\:_{x\to\:+(-2)}(\frac{8}{x})
taylor 9xln(1+2x)	taylor\:9x\ln(1+2x)
y^{(1/2)}(dy)/(dx)+y^{(3/2)}=1,y(0)=4	y^{(\frac{1}{2})}\frac{dy}{dx}+y^{(\frac{3}{2})}=1,y(0)=4
derivative of ln(x+y^2)	\frac{d}{dx}(\ln(x+y^{2}))
derivative of ln\|sec(x+tan(x)\|)	\frac{d}{dx}(\ln\left\|\sec(x)+\tan(x)\right\|)
x(dy)/(dx)=y^2-y,y(1/4)= 1/4	x\frac{dy}{dx}=y^{2}-y,y(\frac{1}{4})=\frac{1}{4}
derivative of x^2+ax+b	derivative\:x^{2}+ax+b
(\partial)/(\partial x)((e^x)/(y+x^7))	\frac{\partial\:}{\partial\:x}(\frac{e^{x}}{y+x^{7}})
tangent of 4x^3-18x^2-48x	tangent\:4x^{3}-18x^{2}-48x
derivative of 4-2x	\frac{d}{dx}(4-2x)
area 2y=x,(y^2)/2 =x	area\:2y=x,\frac{y^{2}}{2}=x
derivative of arcsec(x+2)	\frac{d}{dx}(\arcsec(x+2))
limit as x approaches infinity of 1/(-x)	\lim\:_{x\to\:\infty\:}(\frac{1}{-x})
integral of (2x^3-2/3 x^2+5x)	\int\:(2x^{3}-\frac{2}{3}x^{2}+5x)dx
integral of 1/(sqrt(x^2+20x))	\int\:\frac{1}{\sqrt{x^{2}+20x}}dx
(\partial)/(\partial x)(2x-sqrt(3y^2+z^2))	\frac{\partial\:}{\partial\:x}(2x-\sqrt{3y^{2}+z^{2}})
derivative of (14/(x^3))	\frac{d}{dx}(\frac{14}{x^{3}})
(\partial)/(\partial x)(x^{x/y}cos(x/y))	\frac{\partial\:}{\partial\:x}(x^{\frac{x}{y}}\cos(\frac{x}{y}))
sum from n=1 to infinity of 1/((5n-4)^4)	\sum\:_{n=1}^{\infty\:}\frac{1}{(5n-4)^{4}}
integral of-0.4x^2+1000	\int\:-0.4x^{2}+1000dx
(\partial}{\partial x}(ln(\frac{y^2)/x))	\frac{\partial\:}{\partial\:x}(\ln(\frac{y^{2}}{x}))
derivative of (x-4)^3+3x(x-4)^2	derivative\:(x-4)^{3}+3x(x-4)^{2}
limit as x approaches-infinity of x^6	\lim\:_{x\to\:-\infty\:}(x^{6})
(\partial)/(\partial x)(-4cos(3x))	\frac{\partial\:}{\partial\:x}(-4\cos(3x))
integral of (12s+12)/((s^2+1)(s-1)^3)	\int\:\frac{12s+12}{(s^{2}+1)(s-1)^{3}}ds
integral of 1/(4-x^2)	\int\:\frac{1}{4-x^{2}}dx
(dy)/(dx)=(-(3y)/(3x+2y))	\frac{dy}{dx}=(-\frac{3y}{3x+2y})
-6y^{''}+24y=0	-6y^{\prime\:\prime\:}+24y=0
(\partial)/(\partial y)(xye^{xz})	\frac{\partial\:}{\partial\:y}(xye^{xz})
limit as x approaches-infinity of x^2+2x	\lim\:_{x\to\:-\infty\:}(x^{2}+2x)
(d^2x)/(dx^2)	\frac{d^{2}x}{dx^{2}}
derivative of-(15x^4/2+(6x^2)/5-x/3-4)	\frac{d}{dx}(-\frac{15x^{4}}{2}+\frac{6x^{2}}{5}-\frac{x}{3}-4)
integral of xcos^3(x)	\int\:x\cos^{3}(x)dx
limit as x approaches 0 of (ln(1+1/x))/x	\lim\:_{x\to\:0}(\frac{\ln(1+\frac{1}{x})}{x})

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