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Popular Calculus Problems

y^'+3x^{-1}y=x^2	y^{\prime\:}+3x^{-1}y=x^{2}
integral from 1 to 2 of x^4ln(x)	\int\:_{1}^{2}x^{4}\ln(x)dx
(\partial)/(\partial x)(y^2tan(xy))	\frac{\partial\:}{\partial\:x}(y^{2}\tan(xy))
derivative of 5e^{2x}	derivative\:5e^{2x}
derivative of 6x^{-1}	\frac{d}{dx}(6x^{-1})
derivative of 5(x^6-8)^5	derivative\:5(x^{6}-8)^{5}
tangent of f(x)=4x+3x^2,\at x=2	tangent\:f(x)=4x+3x^{2},\at\:x=2
(\partial)/(\partial x)(x^2z^2)	\frac{\partial\:}{\partial\:x}(x^{2}z^{2})
derivative of e^{(cos(t)+ln(t))}	derivative\:e^{(\cos(t)+\ln(t))}
(\partial)/(\partial x)(e^{t-x}+e^{w-1})	\frac{\partial\:}{\partial\:x}(e^{t-x}+e^{w-1})
integral of cos(6x)cos(5x)	\int\:\cos(6x)\cos(5x)dx
derivative of g(t)=(t-sqrt(t))/(t^{1/5)}	derivative\:g(t)=\frac{t-\sqrt{t}}{t^{\frac{1}{5}}}
(dy)/(dx)=((2cos(2x)))/(3+2y)	\frac{dy}{dx}=\frac{(2\cos(2x))}{3+2y}
limit as x approaches infinity of 1/(2x)	\lim\:_{x\to\:\infty\:}(\frac{1}{2x})
derivative of ln(ln(2x^3))	\frac{d}{dx}(\ln(\ln(2x^{3})))
(\partial)/(\partial y)((x+y)e^x)	\frac{\partial\:}{\partial\:y}((x+y)e^{x})
derivative of (sqrt(x)-6)/(sqrt(x)+6)	derivative\:\frac{\sqrt{x}-6}{\sqrt{x}+6}
d/(dt)((cosh(t))/(sqrt(cosh(2t)+1)))	\frac{d}{dt}(\frac{\cosh(t)}{\sqrt{\cosh(2t)+1}})
f(x)=(x^2+3)/x	f(x)=\frac{x^{2}+3}{x}
laplacetransform 7+3t+2t^2-5t^3	laplacetransform\:7+3t+2t^{2}-5t^{3}
derivative of 4/(sqrt(x+7))	\frac{d}{dx}(\frac{4}{\sqrt{x}+7})
(dy)/(dt)=2y-1	\frac{dy}{dt}=2y-1
tangent of y= 2/((x-2))	tangent\:y=\frac{2}{(x-2)}
integral from 0 to 6 of pi(sqrt(x-1))^2	\int\:_{0}^{6}π(\sqrt{x-1})^{2}dx
integral of 1/(1-x^2)	\int\:\frac{1}{1-x^{2}}dx
x^2y^'+8xy=17y^3	x^{2}y^{\prime\:}+8xy=17y^{3}
integral of (2xarcsin(x))/(sqrt(1-x^2))	\int\:\frac{2x\arcsin(x)}{\sqrt{1-x^{2}}}dx
derivative of 1+ln(x)	\frac{d}{dx}(1+\ln(x))
derivative of (2x^3-3x+1(x^2+5x))	\frac{d}{dx}((2x^{3}-3x+1)(x^{2}+5x))
sum from i=1 to infinity of 3(1/4)^{i-1}	\sum\:_{i=1}^{\infty\:}3(\frac{1}{4})^{i-1}
integral from 0 to 1 of e^xtan(e^x)	\int\:_{0}^{1}e^{x}\tan(e^{x})dx
limit as x approaches infinity+of 3^{-x}	\lim\:_{x\to\:\infty\:+}(3^{-x})
limit as x approaches 1 of (in(x))/(x-1)	\lim\:_{x\to\:1}(\frac{in(x)}{x-1})
derivative of y=sqrt(x^2+10x)	derivative\:y=\sqrt{x^{2}+10x}
(dy}{dx}=\frac{x^2-2y)/x ,y(2)=2	\frac{dy}{dx}=\frac{x^{2}-2y}{x},y(2)=2
derivative of 5(2^x)	derivative\:5(2^{x})
integral of (x+2)(x+3)	\int\:(x+2)(x+3)dx
integral from pi/6 to pi/2 of cot(x)	\int\:_{\frac{π}{6}}^{\frac{π}{2}}\cot(x)dx
integral of pixcos(nx)	\int\:πx\cos(nx)dx
derivative of 2x^{4/3}-3x^{2/3}	\frac{d}{dx}(2x^{\frac{4}{3}}-3x^{\frac{2}{3}})
((1+arctan(x))e^{2x})^'	((1+\arctan(x))e^{2x})^{\prime\:}
(1/y)^'	(\frac{1}{y})^{\prime\:}
y^'=(xy^3)/(sqrt(1+x^2)),y(0)=-1	y^{\prime\:}=\frac{xy^{3}}{\sqrt{1+x^{2}}},y(0)=-1
limit as x approaches 4 of 3x^2-7x+5	\lim\:_{x\to\:4}(3x^{2}-7x+5)
derivative of-(e^{1/x}/(x^2))	\frac{d}{dx}(-\frac{e^{\frac{1}{x}}}{x^{2}})
integral of x/(x+2)	\int\:\frac{x}{x+2}dx
integral of 2cos^3(x)	\int\:2\cos^{3}(x)dx
integral of (2x-1/(8x))^2	\int\:(2x-\frac{1}{8x})^{2}dx
derivative of (x^3/9+3/(4x))	\frac{d}{dx}(\frac{x^{3}}{9}+\frac{3}{4x})
area 9(x^3-x),0	area\:9(x^{3}-x),0
laplacetransform t^2e^{5t}	laplacetransform\:t^{2}e^{5t}
area y=sqrt(x),y=x^3	area\:y=\sqrt{x},y=x^{3}
sum from n=0 to infinity of n(1/3)^n	\sum\:_{n=0}^{\infty\:}n(\frac{1}{3})^{n}
integral of y^2\sqrt[5]{2-4y^3}	\int\:y^{2}\sqrt[5]{2-4y^{3}}dy
limit as x approaches 0 of cos(4/x)	\lim\:_{x\to\:0}(\cos(\frac{4}{x}))
slope of (-3/4 , 1/4),(1/2 ,-3/2)	slope\:(-\frac{3}{4},\frac{1}{4}),(\frac{1}{2},-\frac{3}{2})
area f(x)=x^2-4,g(x)=0,x=-4,x=3	area\:f(x)=x^{2}-4,g(x)=0,x=-4,x=3
(\partial)/(\partial x)(2x-cos(y))	\frac{\partial\:}{\partial\:x}(2x-\cos(y))
derivative of sqrt((sin(x)/(1-sin(x))))	\frac{d}{dx}(\sqrt{\frac{\sin(x)}{1-\sin(x)}})
(\partial)/(\partial y)(sqrt(25-x^2-5y))	\frac{\partial\:}{\partial\:y}(\sqrt{25-x^{2}-5y})
integral of 6xsqrt(1+x^2)	\int\:6x\sqrt{1+x^{2}}dx
y^{''}+20y^'+500y=0	y^{\prime\:\prime\:}+20y^{\prime\:}+500y=0
xdy+ydx=0	xdy+ydx=0
integral of pit-t^2cos(nt)	\int\:πt-t^{2}\cos(nt)dt
inverse oflaplace (2/3)/(s^2+2s+17)	inverselaplace\:\frac{\frac{2}{3}}{s^{2}+2s+17}
derivative of (sqrt(25-x^2))/(32x)	derivative\:\frac{\sqrt{25-x^{2}}}{32x}
integral of (tan(5x)-sec(5x))^2	\int\:(\tan(5x)-\sec(5x))^{2}dx
derivative of 2^{sqrt(x)}	\frac{d}{dx}(2^{\sqrt{x}})
(dy)/(dx)=y^2e^xsin(3x)	\frac{dy}{dx}=y^{2}e^{x}\sin(3x)
derivative of 2/(x^3-1/(x^2))	\frac{d}{dx}(\frac{2}{x^{3}}-\frac{1}{x^{2}})
integral of sin(3t)	\int\:\sin(3t)dt
taylor e^{1/x}	taylor\:e^{\frac{1}{x}}
tangent of f(x)= 1/x ,\at x=1.5	tangent\:f(x)=\frac{1}{x},\at\:x=1.5
integral of (x(x-2))/((x-1)^3)	\int\:\frac{x(x-2)}{(x-1)^{3}}dx
integral from 0 to 5 of x 2/95 (12-x)	\int\:_{0}^{5}x\frac{2}{95}(12-x)dx
derivative of (sqrt(x)/(1+x^2))	\frac{d}{dx}(\frac{\sqrt{x}}{1+x^{2}})
derivative of 4/5 x^{10}	\frac{d}{dx}(\frac{4}{5}x^{10})
tangent of y= 8/(sqrt(x)),(16, 8/4)	tangent\:y=\frac{8}{\sqrt{x}},(16,\frac{8}{4})
derivative of 2/((1-x^3))	\frac{d}{dx}(\frac{2}{(1-x)^{3}})
integral from 0 to 1 of 5(1+sqrt(x))^6	\int\:_{0}^{1}5(1+\sqrt{x})^{6}dx
(\partial)/(\partial x)(xye^{xz})	\frac{\partial\:}{\partial\:x}(xye^{xz})
derivative of arcsec(1/x)	\frac{d}{dx}(\arcsec(\frac{1}{x}))
limit as x approaches-4 of 3x^2-4x+8	\lim\:_{x\to\:-4}(3x^{2}-4x+8)
(\partial)/(\partial z)(x^{y/z})	\frac{\partial\:}{\partial\:z}(x^{\frac{y}{z}})
area cos(x),2-cos(x),[0,2pi]	area\:\cos(x),2-\cos(x),[0,2π]
derivative of-16t^2+44t+31	derivative\:-16t^{2}+44t+31
limit as x approaches 2 of 3x-5	\lim\:_{x\to\:2}(3x-5)
xsqrt(1-y^2dx)=dy	x\sqrt{1-y^{2}dx}=dy
(dy)/(dx)=yxsin(x^2)	\frac{dy}{dx}=yx\sin(x^{2})
integral of 5/(5x+2)	\int\:\frac{5}{5x+2}dx
derivative of (1-ln(x)/(x^2))	\frac{d}{dx}(\frac{1-\ln(x)}{x^{2}})
integral from 0 to ln(11) of xe^x	\int\:_{0}^{\ln(11)}xe^{x}dx
integral of (3-5x^2)	\int\:(3-5x^{2})dx
integral of sin(2-x)	\int\:\sin(2-x)dx
derivative of-(50/(x^2))	\frac{d}{dx}(-\frac{50}{x^{2}})
(\partial)/(\partial x)((2pir^{3/2})/(sqrt(yx)))	\frac{\partial\:}{\partial\:x}(\frac{2πr^{\frac{3}{2}}}{\sqrt{yx}})
area y=x,y=2xsqrt(81-x^2)	area\:y=x,y=2x\sqrt{81-x^{2}}
integral of 1/((x^2-1)^2)	\int\:\frac{1}{(x^{2}-1)^{2}}dx
(\partial)/(\partial y)(7x^{4y})	\frac{\partial\:}{\partial\:y}(7x^{4y})
taylor (x-5)e^{(x)}+5	taylor\:(x-5)e^{(x)}+5

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