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Popular Calculus Problems

derivative of-ke^{l(x-m}+ne^{-p(x-m)}+q)	\frac{d}{dx}(-ke^{l(x-m)}+ne^{-p(x-m)}+q)
inverse oflaplace 1/((s-2)^2+9)	inverselaplace\:\frac{1}{(s-2)^{2}+9}
d/(dj)(6i+10j)	\frac{d}{dj}(6i+10j)
(x+y)dx-(x+y-2)dy=0	(x+y)dx-(x+y-2)dy=0
derivative of (x^2-1(x^2+1))	\frac{d}{dx}((x^{2}-1)(x^{2}+1))
derivative of sin^2(2x)	derivative\:\sin^{2}(2x)
integral of (1-x)/(e^x)	\int\:\frac{1-x}{e^{x}}dx
integral of tsec^2(2t)	\int\:t\sec^{2}(2t)dt
(\partial)/(\partial y)(y/((x+y)^2))	\frac{\partial\:}{\partial\:y}(\frac{y}{(x+y)^{2}})
derivative of (3x^2+ln(x)(5x^3)^x)	\frac{d}{dx}((3x^{2}+\ln(x))(5x^{3})^{x})
derivative of f(t)=t^{5/3}e^t	derivative\:f(t)=t^{\frac{5}{3}}e^{t}
integral from 0 to infinity of e^{-x}cos(x)	\int\:_{0}^{\infty\:}e^{-x}\cos(x)dx
(\partial)/(\partial x)(e^{-2t}cos(pix))	\frac{\partial\:}{\partial\:x}(e^{-2t}\cos(πx))
(dy)/(dt)= t/(ye^{y+t^2)}	\frac{dy}{dt}=\frac{t}{ye^{y+t^{2}}}
derivative of sin^4(3xtan^3(4x))	\frac{d}{dx}(\sin^{4}(3x)\tan^{3}(4x))
integral of (x^2)/(sqrt(a^2+(x-b)^2))	\int\:\frac{x^{2}}{\sqrt{a^{2}+(x-b)^{2}}}dx
integral of 5xcos(8x)	\int\:5x\cos(8x)dx
derivative of 2pisqrt((0.5/(9.8)))	\frac{d}{dx}(2π\sqrt{\frac{0.5}{9.8}})
sqrt(2xy)(dy)/(dx)=1	\sqrt{2xy}\frac{dy}{dx}=1
derivative of f(x)=x^3(x-4)^2	derivative\:f(x)=x^{3}(x-4)^{2}
derivative of-2x(e^{-2x})	\frac{d}{dx}(-2x(e^{-2x}))
derivative of (1-e^{2x}/(1+e^{2x)})	\frac{d}{dx}(\frac{1-e^{2x}}{1+e^{2x}})
integral of (cos(x))/(1-sin^2(x))	\int\:\frac{\cos(x)}{1-\sin^{2}(x)}dx
integral of ((x-2))/1	\int\:\frac{(x-2)}{1}dx
derivative of 9arctan(x+sqrt(1+x^2))	\frac{d}{dx}(9\arctan(x+\sqrt{1+x^{2}}))
limit as x approaches 4 of (4x)/(x-4)	\lim\:_{x\to\:4}(\frac{4x}{x-4})
integral of (sin(x))/(x^2)	\int\:\frac{\sin(x)}{x^{2}}dx
integral of (x+1)/(2x^2+4x+5)	\int\:\frac{x+1}{2x^{2}+4x+5}dx
y^'=ysin(2x),y(0)=1.6	y^{\prime\:}=y\sin(2x),y(0)=1.6
integral of (16)/(x^2)	\int\:\frac{16}{x^{2}}dx
derivative of 2e^x+4/(\sqrt[3]{x)}	derivative\:2e^{x}+\frac{4}{\sqrt[3]{x}}
integral from 0 to 4 of x^2sqrt(16-x^2)	\int\:_{0}^{4}x^{2}\sqrt{16-x^{2}}dx
(dy)/(dx)-xy^2=2xy	\frac{dy}{dx}-xy^{2}=2xy
sum from n=0 to infinity of 1/(2^{2n)}	\sum\:_{n=0}^{\infty\:}\frac{1}{2^{2n}}
integral of 1/6 e^{6x}	\int\:\frac{1}{6}e^{6x}dx
limit as x approaches 3 of x^2-3x-10	\lim\:_{x\to\:3}(x^{2}-3x-10)
integral of (x^2-16x+9)/(x^4+10x^2+9)	\int\:\frac{x^{2}-16x+9}{x^{4}+10x^{2}+9}dx
derivative of y= 3/2 x	derivative\:y=\frac{3}{2}x
limit as x approaches 0 of (2^x)/x	\lim\:_{x\to\:0}(\frac{2^{x}}{x})
limit as x approaches 0+of 9sin(x)ln(x)	\lim\:_{x\to\:0+}(9\sin(x)\ln(x))
limit as x approaches 0-of-1/(3x^3)	\lim\:_{x\to\:0-}(-\frac{1}{3x^{3}})
integral from 0 to pi/9 of 7-7cos(3x)	\int\:_{0}^{\frac{π}{9}}7-7\cos(3x)dx
limit as x approaches 1 of-x/(x^2-x)	\lim\:_{x\to\:1}(-\frac{x}{x^{2}-x})
derivative of f(x)=(csc(3x-1))^{2/3}	derivative\:f(x)=(\csc(3x-1))^{\frac{2}{3}}
integral of (sqrt(15y^2-2))/(y^2)	\int\:\frac{\sqrt{15y^{2}-2}}{y^{2}}dy
derivative of f(x)=6tan(x)	derivative\:f(x)=6\tan(x)
integral of sqrt(x^2+2x)	\int\:\sqrt{x^{2}+2x}dx
(d^2)/(dx^2)(1/(x^7))	\frac{d^{2}}{dx^{2}}(\frac{1}{x^{7}})
sum from n=1 to infinity of 5/(sqrt(n))	\sum\:_{n=1}^{\infty\:}\frac{5}{\sqrt{n}}
integral of (4(sec(θ))^2-sin(θ))	\int\:(4(\sec(θ))^{2}-\sin(θ))dθ
limit as x approaches 3 of (x+4)/(x+7)	\lim\:_{x\to\:3}(\frac{x+4}{x+7})
integral from 0 to 1 of (x^2+3x+4)	\int\:_{0}^{1}(x^{2}+3x+4)dx
limit as x approaches-3 of (3-x)/(3+x)	\lim\:_{x\to\:-3}(\frac{3-x}{3+x})
derivative of 2(ln(x)+1)	derivative\:2(\ln(x)+1)
integral of 1/(x^e)	\int\:\frac{1}{x^{e}}dx
derivative of y=6log_{5}(x^2-6)	derivative\:y=6\log_{5}(x^{2}-6)
derivative of y=(5-2x^3)^3	derivative\:y=(5-2x^{3})^{3}
integral of 2^xx^2	\int\:2^{x}x^{2}dx
integral of x^5sqrt(x^6+3)	\int\:x^{5}\sqrt{x^{6}+3}dx
derivative of f(x)=(e^x)/(-8x^7)	derivative\:f(x)=\frac{e^{x}}{-8x^{7}}
y^'+y=te^{-t}+e^t	y^{\prime\:}+y=te^{-t}+e^{t}
limit as x approaches 0 of ln(x/(x-1))	\lim\:_{x\to\:0}(\ln(\frac{x}{x-1}))
inverse oflaplace (e^{-s})/(s-8)	inverselaplace\:\frac{e^{-s}}{s-8}
integral of sqrt(4-2x)	\int\:\sqrt{4-2x}dx
2x-y(dy)/(dx)=3	2x-y\frac{dy}{dx}=3
integral of (sqrt(x^2+1))/(x^4)	\int\:\frac{\sqrt{x^{2}+1}}{x^{4}}dx
derivative of 500-500t^{-1}	derivative\:500-500t^{-1}
taylor sqrt(2+x),-1	taylor\:\sqrt{2+x},-1
integral of ((8x^2-5x+1))/(x^2+x)	\int\:\frac{(8x^{2}-5x+1)}{x^{2}+x}dx
integral of (11)/(x^3-27)	\int\:\frac{11}{x^{3}-27}dx
integral of x^2(5x^3-1)^{3/2}	\int\:x^{2}(5x^{3}-1)^{\frac{3}{2}}dx
derivative of (-3x^5-x^4-x^3+4x^2/(x^2))	\frac{d}{dx}(\frac{-3x^{5}-x^{4}-x^{3}+4x^{2}}{x^{2}})
y^{''}+4y^'+4y=0,y(0)=-1,y^'(0)=0	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=0,y(0)=-1,y^{\prime\:}(0)=0
limit as x approaches-4 of sqrt(-2x+3)	\lim\:_{x\to\:-4}(\sqrt{-2x+3})
(\partial)/(\partial x)((4x-2y)/(2x^2+3y))	\frac{\partial\:}{\partial\:x}(\frac{4x-2y}{2x^{2}+3y})
derivative of 5/(x^2+25)	\frac{d}{dx}(\frac{5}{x^{2}+25})
integral of 5sin(x)sqrt(5-cos(x))	\int\:5\sin(x)\sqrt{5-\cos(x)}dx
integral from 0 to 4 of 1/(x^2+x-6)	\int\:_{0}^{4}\frac{1}{x^{2}+x-6}dx
integral from 1 to 4 of (4x^2+sqrt(x))	\int\:_{1}^{4}(4x^{2}+\sqrt{x})dx
integral of 1/(1-5t)	\int\:\frac{1}{1-5t}dt
(\partial)/(\partial x)(x^3*4x+5y)	\frac{\partial\:}{\partial\:x}(x^{3}\cdot\:4x+5y)
derivative of y=x(x-4)	derivative\:y=x(x-4)
derivative of sin(x+cos(2x))	\frac{d}{dx}(\sin(x)+\cos(2x))
integral from 0 to 2 of \|x-1\|	\int\:_{0}^{2}\left\|x-1\right\|dx
integral from 0 to infinity of 5/(x^2+4)	\int\:_{0}^{\infty\:}\frac{5}{x^{2}+4}dx
integral of cos(8x^2)	\int\:\cos(8x^{2})dx
(\partial)/(\partial x)(-sqrt(x))	\frac{\partial\:}{\partial\:x}(-\sqrt{x})
integral from 0 to 4 of 2x	\int\:_{0}^{4}2xdx
y^{''}-4y^'=7x+1	y^{\prime\:\prime\:}-4y^{\prime\:}=7x+1
(\partial)/(\partial x)(e^{4x}cos(7y))	\frac{\partial\:}{\partial\:x}(e^{4x}\cos(7y))
d/(dy)(y^{-1})	\frac{d}{dy}(y^{-1})
derivative of x^2e^x-3	\frac{d}{dx}(x^{2}e^{x}-3)
limit as x approaches 0 of x*arctan(1/x)	\lim\:_{x\to\:0}(x\cdot\:\arctan(\frac{1}{x}))
integral of (2x^3+3x+1)^4(6x^2+3)	\int\:(2x^{3}+3x+1)^{4}(6x^{2}+3)dx
integral of 1/(x(1+x^2))	\int\:\frac{1}{x(1+x^{2})}dx
(ln(1-x^2))^'	(\ln(1-x^{2}))^{\prime\:}
derivative of cos(ysqrt(x^2+1))	\frac{d}{dx}(\cos(y\sqrt{x^{2}+1}))
xy^2y^'=y^3-2x^3	xy^{2}y^{\prime\:}=y^{3}-2x^{3}
derivative of sqrt(20-25sin^2(x))	\frac{d}{dx}(\sqrt{20-25\sin^{2}(x)})
derivative of 1/(4+3x)	\frac{d}{dx}(\frac{1}{4+3x})

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