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Popular Calculus Problems

derivative of (e^{2x}-1/(e^{2x)+1})	\frac{d}{dx}(\frac{e^{2x}-1}{e^{2x}+1})
y^{''}+14y^'+100y=10sin(2pix)+5sin(pix)	y^{\prime\:\prime\:}+14y^{\prime\:}+100y=10\sin(2π\cdot\:x)+5\sin(π\cdot\:x)
integral of 1/((x^2+1)^2(x^2-1))	\int\:\frac{1}{(x^{2}+1)^{2}(x^{2}-1)}dx
3y^{''}+y^'+2y=0	3y^{\prime\:\prime\:}+y^{\prime\:}+2y=0
integral of (4x^2)/(sqrt(x^3+8))	\int\:\frac{4x^{2}}{\sqrt{x^{3}+8}}dx
(\partial)/(\partial x)((1-x-4y)^{1/2})	\frac{\partial\:}{\partial\:x}((1-x-4y)^{\frac{1}{2}})
(\partial)/(\partial x)(5e^{x^5y})	\frac{\partial\:}{\partial\:x}(5e^{x^{5}y})
derivative of f(x)=(x^2+2x+1)/(x^2-2x+1)	derivative\:f(x)=\frac{x^{2}+2x+1}{x^{2}-2x+1}
integral of 7sin(5x)sin(x)	\int\:7\sin(5x)\sin(x)dx
limit as x approaches 0 of 4x-\|x\|	\lim\:_{x\to\:0}(4x-\left\|x\right\|)
integral of-xe^{(-x^2)/2}	\int\:-xe^{\frac{-x^{2}}{2}}dx
x^{''}-5x^'+6x=cos(t)*e^{-t}	x^{\prime\:\prime\:}-5x^{\prime\:}+6x=\cos(t)\cdot\:e^{-t}
(\partial)/(\partial x)((u^2)/(x^2))	\frac{\partial\:}{\partial\:x}(\frac{u^{2}}{x^{2}})
(\partial)/(\partial x)(-4/(x^4\sqrt[4]{x)})	\frac{\partial\:}{\partial\:x}(-\frac{4}{x^{4}\sqrt[4]{x}})
(xdy)/(dx)+3y=x^3-x	\frac{xdy}{dx}+3y=x^{3}-x
y^'=2y^2+xy^2,y(0)=1	y^{\prime\:}=2y^{2}+xy^{2},y(0)=1
derivative of 1/(5-2x)	\frac{d}{dx}(\frac{1}{5-2x})
integral of (9-162x)/(sqrt(64-81x^2))	\int\:\frac{9-162x}{\sqrt{64-81x^{2}}}dx
integral of-2x*ln(x)	\int\:-2x\cdot\:\ln(x)dx
tangent of x^2-1/x	tangent\:x^{2}-\frac{1}{x}
integral from 3 to 6 of (2x-3)/6	\int\:_{3}^{6}\frac{2x-3}{6}dx
integral from 0 to pi of x*sin^2(x)	\int\:_{0}^{π}x\cdot\:\sin^{2}(x)dx
y^{''}-y^'-6y=0,y(0)=1,y^'(0)=-1	y^{\prime\:\prime\:}-y^{\prime\:}-6y=0,y(0)=1,y^{\prime\:}(0)=-1
integral of ((3x^2))/2	\int\:\frac{(3x^{2})}{2}dx
derivative of e^{x^2+6x}	\frac{d}{dx}(e^{x^{2}+6x})
integral of (5x+1)^4	\int\:(5x+1)^{4}dx
(d^2)/(dx^2)(1/(x^2+1))	\frac{d^{2}}{dx^{2}}(\frac{1}{x^{2}+1})
derivative of f(x)=9-\|x-4\|\at x	derivative\:f(x)=9-\left\|x-4\right\|\at\:x
limit as x approaches 5-of 2/(x^2-25)	\lim\:_{x\to\:5-}(\frac{2}{x^{2}-25})
integral of (10)/((x+1)(x^2+9))	\int\:\frac{10}{(x+1)(x^{2}+9)}dx
simplify (e^{-x}-e^2)(e^x+e^{-5})	simplify\:(e^{-x}-e^{2})(e^{x}+e^{-5})
slope of (2,0),(32,-5)	slope\:(2,0),(32,-5)
integral of 27sec^4(x)	\int\:27\sec^{4}(x)dx
integral of (cot^5(x))/(sqrt(sin(x)))	\int\:\frac{\cot^{5}(x)}{\sqrt{\sin(x)}}dx
limit as x approaches-3 of x	\lim\:_{x\to\:-3}(x)
integral of (sin(x)+cos(x))/(sin^2(x))	\int\:\frac{\sin(x)+\cos(x)}{\sin^{2}(x)}dx
integral of arcosin(x)	\int\:arco\sin(x)dx
tangent of x^2-3	tangent\:x^{2}-3
f(x)=x^2-cos(2x)	f(x)=x^{2}-\cos(2x)
derivative of ln((x^2+1^2))	\frac{d}{dx}(\ln((x^{2}+1)^{2}))
tangent of y=x^2-5,(2,-1)	tangent\:y=x^{2}-5,(2,-1)
area 1/x ,\sqrt[3]{x},1,8	area\:\frac{1}{x},\sqrt[3]{x},1,8
(\partial)/(\partial x)(x*ln(2y))	\frac{\partial\:}{\partial\:x}(x\cdot\:\ln(2y))
limit as x approaches 0 of (2x)/(ln(x))	\lim\:_{x\to\:0}(\frac{2x}{\ln(x)})
tangent of 4x(x^2-4)	tangent\:4x(x^{2}-4)
normal of g(x)=x^4-6/x ,(2,13)	normal\:g(x)=x^{4}-\frac{6}{x},(2,13)
tangent of 4cot^7(x),\at x= pi/4	tangent\:4\cot^{7}(x),\at\:x=\frac{π}{4}
(\partial)/(\partial y)(2y^2x)	\frac{\partial\:}{\partial\:y}(2y^{2}x)
limit as x approaches 8 of (3x^2-24x)/(x^2-64)	\lim\:_{x\to\:8}(\frac{3x^{2}-24x}{x^{2}-64})
limit as x approaches 2 of ((x+1))/(x-2)	\lim\:_{x\to\:2}(\frac{(x+1)}{x-2})
derivative of 2x-sin(2x)	\frac{d}{dx}(2x-\sin(2x))
tangent of f(x)= 2/(sqrt(x)),\at x= 1/16	tangent\:f(x)=\frac{2}{\sqrt{x}},\at\:x=\frac{1}{16}
integral of 1/(x*(ln(x))^p)	\int\:\frac{1}{x\cdot\:(\ln(x))^{p}}dx
(dy)/(dx)=-11	\frac{dy}{dx}=-11
derivative of f(x)=3x^2-x+5	derivative\:f(x)=3x^{2}-x+5
limit as x approaches-2-of (1-x)/(x^2-4)	\lim\:_{x\to\:-2-}(\frac{1-x}{x^{2}-4})
sum from n=1 to infinity of 3^nx^nn!	\sum\:_{n=1}^{\infty\:}3^{n}x^{n}n!
integral of (x-1)^9	\int\:(x-1)^{9}dx
slope ofintercept (-3,5),(-1,-4)	slopeintercept\:(-3,5),(-1,-4)
(\partial)/(\partial u)(1/3 (u+v))	\frac{\partial\:}{\partial\:u}(\frac{1}{3}(u+v))
integral of-sin(3t)	\int\:-\sin(3t)dt
derivative of ln(2x^2)	\frac{d}{dx}(\ln(2x^{2}))
integral of 9(x+7)^2ln(x+7)	\int\:9(x+7)^{2}\ln(x+7)dx
integral of (7x+6)/(x^9)	\int\:\frac{7x+6}{x^{9}}dx
integral of (x^3-x)/((x^4-2x^2+3)^2)	\int\:\frac{x^{3}-x}{(x^{4}-2x^{2}+3)^{2}}dx
integral of 2t^{-4}	\int\:2t^{-4}dt
derivative of x^6-3x^5+10x^3-15x^2+9x-2	\frac{d}{dx}(x^{6}-3x^{5}+10x^{3}-15x^{2}+9x-2)
integral of x^3sqrt(49-x^2)	\int\:x^{3}\sqrt{49-x^{2}}dx
derivative of a(2xe^{3x}+e^{3x}*3x^2)	\frac{d}{dx}(a(2xe^{3x}+e^{3x}\cdot\:3x^{2}))
integral of 8sin^2(pix)cos^5(pix)	\int\:8\sin^{2}(πx)\cos^{5}(πx)dx
(x^2sin(x)+4y)dx+(x)dy=0	(x^{2}\sin(x)+4y)dx+(x)dy=0
integral of ln(x+sqrt((x^2-1)))	\int\:\ln(x+\sqrt{(x^{2}-1)})dx
parity ln(sec(x)+tan(x))	parity\:\ln(\sec(x)+\tan(x))
integral of sqrt(1+9sin^2(3x))	\int\:\sqrt{1+9\sin^{2}(3x)}dx
limit as x approaches 0 of ((x^2-4x))/x	\lim\:_{x\to\:0}(\frac{(x^{2}-4x)}{x})
integral of-e^x(x+1)	\int\:-e^{x}(x+1)dx
inverse oflaplace 1/(s^2+s^2)	inverselaplace\:\frac{1}{s^{2}+s^{2}}
limit as x approaches 6 of cos(x*pi)	\lim\:_{x\to\:6}(\cos(x\cdot\:π))
(\partial)/(\partial x)(I/(2x))	\frac{\partial\:}{\partial\:x}(\frac{I}{2x})
(\partial)/(\partial x)(2x^2e^y)	\frac{\partial\:}{\partial\:x}(2x^{2}e^{y})
derivative of (x^2+4^{-2})	\frac{d}{dx}((x^{2}+4)^{-2})
(dy)/(dt)=b(1-y)y	\frac{dy}{dt}=b(1-y)y
limit as x approaches-9+of 3x^2-4x-7	\lim\:_{x\to\:-9+}(3x^{2}-4x-7)
integral of sin(θ)(cot(θ)+csc(θ))	\int\:\sin(θ)(\cot(θ)+\csc(θ))dθ
(\partial)/(\partial x)(6x+6y^2)	\frac{\partial\:}{\partial\:x}(6x+6y^{2})
derivative of sqrt(x){f}(x)	\frac{d}{dx}(\sqrt{x}{f}(x))
((dy)/(dx))=sqrt(y+2x+5)-2	(\frac{dy}{dx})=\sqrt{y+2x+5}-2
5y^{''}+y^'=-4x	5y^{\prime\:\prime\:}+y^{\prime\:}=-4x
integral of (5x^4)/(1+x^{10)}	\int\:\frac{5x^{4}}{1+x^{10}}dx
integral of sqrt(x^2-6x+10)	\int\:\sqrt{x^{2}-6x+10}dx
y^{''}-5y^'=(8t-7)sin(2t)	y^{\prime\:\prime\:}-5y^{\prime\:}=(8t-7)\sin(2t)
limit as x approaches 7 of x(x-2)	\lim\:_{x\to\:7}(x(x-2))
derivative of cos(5x^2+7x-1)	\frac{d}{dx}(\cos(5x^{2}+7x-1))
derivative of 2x*cos(x^2)	derivative\:2x\cdot\:\cos(x^{2})
integral of 1/(10^x)	\int\:\frac{1}{10^{x}}dx
integral of (x^4)/(3355)	\int\:\frac{x^{4}}{3355}dx
y^{''}+2y^'-3y=e^{-x}	y^{\prime\:\prime\:}+2y^{\prime\:}-3y=e^{-x}
derivative of y=(e^x)/(x^2)	derivative\:y=\frac{e^{x}}{x^{2}}
integral of-sin^2(x)cos(x)	\int\:-\sin^{2}(x)\cos(x)dx
derivative of (x+3/x)	\frac{d}{dx}(\frac{x+3}{x})

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