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Popular Calculus Problems

(dy)/(dx)=0.1y(1-y/(500))	\frac{dy}{dx}=0.1y(1-\frac{y}{500})
9y^{''}-24y^'+16y=0	9y^{\prime\:\prime\:}-24y^{\prime\:}+16y=0
derivative of y= 1/((x^2-2)(x^2+x+5))	derivative\:y=\frac{1}{(x^{2}-2)(x^{2}+x+5)}
tangent of y=5xcos(x),(pi,-5pi)	tangent\:y=5x\cos(x),(π,-5π)
derivative of y=csc^3(2x)	derivative\:y=\csc^{3}(2x)
derivative of (ax+be^{-x})	\frac{d}{dx}((ax+b)e^{-x})
integral of [sqrt(x)(x^2-1)+csc^2(x)]	\int\:[\sqrt{x}(x^{2}-1)+\csc^{2}(x)]dx
derivative of 4sin(x)sin(x)	derivative\:4\sin(x)\sin(x)
inverse oflaplace (s+5)/(s^2+5s+9)	inverselaplace\:\frac{s+5}{s^{2}+5s+9}
y^{''}+4y=t^2+3e^t,y(0)=0,y^'(0)=2	y^{\prime\:\prime\:}+4y=t^{2}+3e^{t},y(0)=0,y^{\prime\:}(0)=2
integral of y^3	\int\:y^{3}dy
tangent of y=(((x-1))/((x+1)))^2,\at x=0	tangent\:y=(\frac{(x-1)}{(x+1)})^{2},\at\:x=0
2(dy)/(dx)+10y=1	2\frac{dy}{dx}+10y=1
integral from 0 to 3 of 9-x^2	\int\:_{0}^{3}9-x^{2}dx
integral of ((3x+5))/((x^2+2x+2)^2)	\int\:\frac{(3x+5)}{(x^{2}+2x+2)^{2}}dx
xln(x)y^'+y=xe^x,y(2)=-5	x\ln(x)y^{\prime\:}+y=xe^{x},y(2)=-5
derivative of 5xsqrt(x)	\frac{d}{dx}(5x\sqrt{x})
derivative of 2cos(1/2 x)	\frac{d}{dx}(2\cos(\frac{1}{2}x))
integral from 0 to pi/4 of cos(x)	\int\:_{0}^{\frac{π}{4}}\cos(x)dx
derivative of 20x^{-8}+5x^{-3}-7x^{-7}	\frac{d}{dx}(20x^{-8}+5x^{-3}-7x^{-7})
derivative of 1/(sqrt(x^2-9y^2))	\frac{d}{dx}(\frac{1}{\sqrt{x^{2}-9y^{2}}})
derivative of (1-x^2^{10})	\frac{d}{dx}((1-x^{2})^{10})
integral of (1+x^2)^{-1/2}	\int\:(1+x^{2})^{-\frac{1}{2}}dx
slope of (-2/7 , 2/3),(5/7 ,-7/3)	slope\:(-\frac{2}{7},\frac{2}{3}),(\frac{5}{7},-\frac{7}{3})
limit as x approaches 1 of (x-1)/(x^n-1)	\lim\:_{x\to\:1}(\frac{x-1}{x^{n}-1})
(x+y)^2dx+(2xy+x^2-4)dy=0	(x+y)^{2}dx+(2xy+x^{2}-4)dy=0
derivative of 5e^x+3	\frac{d}{dx}(5e^{x}+3)
derivative of (x^2+4e^{-2x})	\frac{d}{dx}((x^{2}+4)e^{-2x})
(x^2-1)((dy)/(dx))=2y	(x^{2}-1)(\frac{dy}{dx})=2y
area x-y^2=0,x+2y^2=3	area\:x-y^{2}=0,x+2y^{2}=3
(\partial)/(\partial x)(x^2y^2z^2)	\frac{\partial\:}{\partial\:x}(x^{2}y^{2}z^{2})
tangent of f(x)=sqrt(7x+4),(3,5)	tangent\:f(x)=\sqrt{7x+4},(3,5)
derivative of cot^2(xcsc(x))	\frac{d}{dx}(\cot^{2}(x)\csc(x))
integral of xsin(6x^2+2)	\int\:x\sin(6x^{2}+2)dx
integral of 1/(x^2yz)	\int\:\frac{1}{x^{2}yz}dx
taylor ln(4-3x)	taylor\:\ln(4-3x)
xy^2y^'=x+3	xy^{2}y^{\prime\:}=x+3
integral of x^3ln(x^3)	\int\:x^{3}\ln(x^{3})dx
y^'= 1/(sec^2(y))	y^{\prime\:}=\frac{1}{\sec^{2}(y)}
derivative of (sin(3x)/(cos(3x)))	\frac{d}{dx}(\frac{\sin(3x)}{\cos(3x)})
limit as x approaches 2 of e^{2x-x^2}	\lim\:_{x\to\:2}(e^{2x-x^{2}})
integral of ye^z	\int\:ye^{z}dz
integral of (sqrt(x^4+1))/(x^3)	\int\:\frac{\sqrt{x^{4}+1}}{x^{3}}dx
limit as x approaches 3 of 2/((x-3)^3)	\lim\:_{x\to\:3}(\frac{2}{(x-3)^{3}})
integral of 1/(x^2\sqrt[5]{x^2)}	\int\:\frac{1}{x^{2}\sqrt[5]{x^{2}}}dx
limit as x approaches 1 of (sqrt(17-x^2)-4)/(x-1)	\lim\:_{x\to\:1}(\frac{\sqrt{17-x^{2}}-4}{x-1})
partialfraction (x^2)/(18x-9)	partialfraction\:\frac{x^{2}}{18x-9}
derivative of 4/5 x^{15}	\frac{d}{dx}(\frac{4}{5}x^{15})
slope of (10.9)(40.3)	slope\:(10.9)(40.3)
integral of sin(2pi)x	\int\:\sin(2π)xdx
integral of 1/((x^4+1))	\int\:\frac{1}{(x^{4}+1)}dx
integral of 5/(x^2+1)	\int\:\frac{5}{x^{2}+1}dx
integral of sec(x/2)	\int\:\sec(\frac{x}{2})dx
derivative of 7e^x+4/(\sqrt[3]{x)}	derivative\:7e^{x}+\frac{4}{\sqrt[3]{x}}
tangent of f(x)=110x-16x^2,\at 3.438	tangent\:f(x)=110x-16x^{2},\at\:3.438
derivative of (x^4-16x^2-16)/((x^2-4)^2)	derivative\:\frac{x^{4}-16x^{2}-16}{(x^{2}-4)^{2}}
xydy-(x^2+y^2)dx=0	xydy-(x^{2}+y^{2})dx=0
sum from n=1 to infinity of 1/((0.8)^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{(0.8)^{n}}
integral from 0 to 2 of x^2sqrt(4-x^2)	\int\:_{0}^{2}x^{2}\sqrt{4-x^{2}}dx
tangent of f(x)=(-8x)/(x^2+1)	tangent\:f(x)=\frac{-8x}{x^{2}+1}
laplacetransform 3t+2	laplacetransform\:3t+2
limit as x approaches-2 of x^2+2x-3	\lim\:_{x\to\:-2}(x^{2}+2x-3)
tangent of 4cos(x)	tangent\:4\cos(x)
2x^2y^'=y^'+5xe^{-y}	2x^{2}y^{\prime\:}=y^{\prime\:}+5xe^{-y}
integral of 4/(sec(x)e^{sin(x))}	\int\:\frac{4}{\sec(x)e^{\sin(x)}}dx
derivative of y=(1+ln(x))^{sin(x)}	derivative\:y=(1+\ln(x))^{\sin(x)}
derivative of (5x^{1/3})	\frac{d}{dx}((5x)^{\frac{1}{3}})
integral from 0 to 8 of x(1/8 x)	\int\:_{0}^{8}x(\frac{1}{8}x)dx
derivative of (x^3-5^5(x^5+7))	\frac{d}{dx}((x^{3}-5)^{5}(x^{5}+7))
derivative of (2x-1)/(2sqrt((x^2-x)))	derivative\:\frac{2x-1}{2\sqrt{(x^{2}-x)}}
derivative of (1/(x^3-2/x)(x^2+x))	\frac{d}{dx}((\frac{1}{x^{3}}-\frac{2}{x})(x^{2}+x))
integral of-2sin(nx)	\int\:-2\sin(nx)dx
tangent of 4x^2=ln(x-y)+3,\at x=0	tangent\:4x^{2}=\ln(x-y)+3,\at\:x=0
integral of e^x(4+e^x)^5	\int\:e^{x}(4+e^{x})^{5}dx
deg2rad (x''+x)^'	deg2rad\:(x\prime\:\prime\:+x)^{\prime\:}
x(dy)/(dx)+y=e^x	x\frac{dy}{dx}+y=e^{x}
integral from 6 to 8 of (94)/((x-6)^3)	\int\:_{6}^{8}\frac{94}{(x-6)^{3}}dx
derivative of (t+5)^{2/3}(2t^2-3)^3	derivative\:(t+5)^{\frac{2}{3}}(2t^{2}-3)^{3}
integral from 0 to pi/(24) of cos(8x)	\int\:_{0}^{\frac{π}{24}}\cos(8x)dx
(\partial)/(\partial x)(26y^2sqrt(x))	\frac{\partial\:}{\partial\:x}(26y^{2}\sqrt{x})
integral of ((sqrt(x)+\sqrt[3]{x})^3)/x	\int\:\frac{(\sqrt{x}+\sqrt[3]{x})^{3}}{x}dx
integral of (e^t)/(sqrt(1-e^{2t))}	\int\:\frac{e^{t}}{\sqrt{1-e^{2t}}}dt
sum from n=0 to infinity of (-1)^n(n+1)	\sum\:_{n=0}^{\infty\:}(-1)^{n}(n+1)
integral of xe^{(-x)}	\int\:xe^{(-x)}dx
derivative of f(x)=e^{ln(x)}-e^{5ln(x^2)}	derivative\:f(x)=e^{\ln(x)}-e^{5\ln(x^{2})}
derivative of f(x)=tan(x)cot(x)	derivative\:f(x)=\tan(x)\cot(x)
derivative of 3/((x-4^2))	\frac{d}{dx}(\frac{3}{(x-4)^{2}})
derivative of arcsin(1/2 x)	\frac{d}{dx}(\arcsin(\frac{1}{2}x))
(\partial)/(\partial x)(arctan(x/3))	\frac{\partial\:}{\partial\:x}(\arctan(\frac{x}{3}))
limit as x approaches-3+of x/(x^2-9)	\lim\:_{x\to\:-3+}(\frac{x}{x^{2}-9})
limit as x approaches 2 of (x^3-8)/(2x)	\lim\:_{x\to\:2}(\frac{x^{3}-8}{2x})
(\partial)/(\partial x)(xe^{xy}-2y+1)	\frac{\partial\:}{\partial\:x}(xe^{xy}-2y+1)
limit as x approaches 3 of cos(1/(x-3))	\lim\:_{x\to\:3}(\cos(\frac{1}{x-3}))
derivative of e^{sqrt(x^2+y^2)}	\frac{d}{dx}(e^{\sqrt{x^{2}+y^{2}}})
derivative of 0.005x^2-ln(x^{16}+70)	\frac{d}{dx}(0.005x^{2}-\ln(x^{16})+70)
derivative of y=(6x^2+8x+2)/(sqrt(x))	derivative\:y=\frac{6x^{2}+8x+2}{\sqrt{x}}
derivative of-4x^{1/2}	derivative\:-4x^{\frac{1}{2}}
simplify x/2 ln((1+x)/(1-x))-1	simplify\:\frac{x}{2}\ln(\frac{1+x}{1-x})-1
(\partial)/(\partial x)((x-1)y^2e^{xy})	\frac{\partial\:}{\partial\:x}((x-1)y^{2}e^{xy})
(dy)/(dx)= y/(2x)	\frac{dy}{dx}=\frac{y}{2x}

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