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Popular Calculus Problems

derivative of 1-2x-3x^2	\frac{d}{dx}(1-2x-3x^{2})
integral of 1/(x^2(9+x^2))	\int\:\frac{1}{x^{2}(9+x^{2})}dx
integral of 5/(x^2sqrt(x^2+4))	\int\:\frac{5}{x^{2}\sqrt{x^{2}+4}}dx
derivative of \sqrt[6]{x}	derivative\:\sqrt[6]{x}
(dy)/(dx)=-5sin(4x)	\frac{dy}{dx}=-5\sin(4x)
integral of 9/(x^2+3x-18)	\int\:\frac{9}{x^{2}+3x-18}dx
integral from-3 to 1 of \|3x+3\|	\int\:_{-3}^{1}\left\|3x+3\right\|dx
x^2y^'=2y^2-x^2	x^{2}y^{\prime\:}=2y^{2}-x^{2}
integral of sinh^2(2x)	\int\:\sinh^{2}(2x)dx
integral of 7/(xln(x))	\int\:\frac{7}{x\ln(x)}dx
(\partial)/(\partial x)((x-4)^2+(y-4)^2-5)	\frac{\partial\:}{\partial\:x}((x-4)^{2}+(y-4)^{2}-5)
(dy)/(dx)=xy^3(1+x^2)^{-1/2},y(0)=1	\frac{dy}{dx}=xy^{3}(1+x^{2})^{-\frac{1}{2}},y(0)=1
(\partial)/(\partial x)(3cos(3x+4y))	\frac{\partial\:}{\partial\:x}(3\cos(3x+4y))
(dy)/(dt)= t/(y-2),y(-1)=0	\frac{dy}{dt}=\frac{t}{y-2},y(-1)=0
integral of sin(x)sin(2x)cos(3x)	\int\:\sin(x)\sin(2x)\cos(3x)dx
(\partial)/(\partial x)((-xy)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{-xy}{x^{2}+y^{2}})
limit as x approaches 3+of (3-x)/(x^2-9)	\lim\:_{x\to\:3+}(\frac{3-x}{x^{2}-9})
(d^2)/(dx^2)f(x)=x^3+3x^2-2x+1	\frac{d^{2}}{dx^{2}}f(x)=x^{3}+3x^{2}-2x+1
(\partial)/(\partial x)(2xye^{xz})	\frac{\partial\:}{\partial\:x}(2xye^{xz})
maclaurin x	maclaurin\:x
2y^{''}+3y^'-y=0	2y^{\prime\:\prime\:}+3y^{\prime\:}-y=0
inverse oflaplace (e^{-4s})/((s-3)^2)	inverselaplace\:\frac{e^{-4s}}{(s-3)^{2}}
derivative of x^2-6	derivative\:x^{2}-6
derivative of f(x)=x-9	derivative\:f(x)=x-9
limit as x approaches 2 of 1/(sqrt(x-2))	\lim\:_{x\to\:2}(\frac{1}{\sqrt{x-2}})
integral of (x^2+4x+1)/(x^3+x)	\int\:\frac{x^{2}+4x+1}{x^{3}+x}dx
derivative of ((x^2-1)/(x^2))	\frac{d}{dx}(\frac{(x^{2}-1)}{x^{2}})
3xdy+4ydx=x^2y^2dx	3xdy+4ydx=x^{2}y^{2}dx
derivative of ln(18x)	\frac{d}{dx}(\ln(18x))
integral of sqrt(2)	\int\:\sqrt{2}dx
derivative of (e^x/(4-3e^x))	\frac{d}{dx}(\frac{e^{x}}{4-3e^{x}})
maclaurin e^{5x}	maclaurin\:e^{5x}
integral of sin(ln(3x))	\int\:\sin(\ln(3x))dx
derivative of 4/(x^2+2)	\frac{d}{dx}(\frac{4}{x^{2}+2})
integral from 0 to ln(2) of e^{2x}	\int\:_{0}^{\ln(2)}e^{2x}dx
integral of 9/2 (t+1)^{1/2}	\int\:\frac{9}{2}(t+1)^{\frac{1}{2}}dt
laplacetransform e^{-1}	laplacetransform\:e^{-1}
integral of-y/(3+y^2)	\int\:-\frac{y}{3+y^{2}}dy
(\partial)/(\partial x)(t^6e^{-x})	\frac{\partial\:}{\partial\:x}(t^{6}e^{-x})
y^{''}+4y=4x	y^{\prime\:\prime\:}+4y=4x
integral of x^2+5x+1	\int\:x^{2}+5x+1dx
derivative of f(x)=(x-sqrt(1-x^2))^2	\frac{d}{dx}f(x)=(x-\sqrt{1-x^{2}})^{2}
derivative of 12cos(2x+pi/6)	\frac{d}{dx}(12\cos(2x+\frac{π}{6}))
limit as t approaches-infinity of e^{3t}	\lim\:_{t\to\:-\infty\:}(e^{3t})
implicit (dy)/(dx),x^2e^y-y^4=e^x	implicit\:\frac{dy}{dx},x^{2}e^{y}-y^{4}=e^{x}
integral of 2x(x^2+7)^8	\int\:2x(x^{2}+7)^{8}dx
derivative of e^xsin(e^x)	\frac{d}{dx}(e^{x}\sin(e^{x}))
d/(dt)(e^{3cos(t)+2t^2})	\frac{d}{dt}(e^{3\cos(t)+2t^{2}})
integral of sec^2(2xy)	\int\:\sec^{2}(2xy)dx
derivative of (x^2-8x+7/(x^2+9))	\frac{d}{dx}(\frac{x^{2}-8x+7}{x^{2}+9})
(\partial)/(\partial x)(t^2e^x+3x^2)	\frac{\partial\:}{\partial\:x}(t^{2}e^{x}+3x^{2})
limit as x approaches 2 of x^2+x-6	\lim\:_{x\to\:2}(x^{2}+x-6)
integral from 0 to pi of sin^3(x)	\int\:_{0}^{π}\sin^{3}(x)dx
inverse oflaplace ((2s+1))/(s(2s+10))	inverselaplace\:\frac{(2s+1)}{s(2s+10)}
derivative of (-x^2-4^2)	\frac{d}{dx}((-x^{2}-4)^{2})
derivative of 3-3x	\frac{d}{dx}(3-3x)
derivative of (1-x/(x^2))	\frac{d}{dx}(\frac{1-x}{x^{2}})
integral of x^2-5x+5	\int\:x^{2}-5x+5dx
integral from pi/2 to pi of 4cot(x/2)	\int\:_{\frac{π}{2}}^{π}4\cot(\frac{x}{2})dx
(\partial)/(\partial x)(y^2e^{2x})	\frac{\partial\:}{\partial\:x}(y^{2}e^{2x})
derivative of e^{x^2-4}+2x+9	\frac{d}{dx}(e^{x^{2}-4}+2x+9)
derivative of tan^4(cot(3x^4+5x))	\frac{d}{dx}(\tan^{4}(\cot(3x^{4}+5x)))
x(dy)/(dx)=x^3+24x^3y	x\frac{dy}{dx}=x^{3}+24x^{3}y
integral of (2cos(x))	\int\:(2\cos(x))dx
(dy)/(dx)=(3sec(y))/((x-3)^2)	\frac{dy}{dx}=\frac{3\sec(y)}{(x-3)^{2}}
(\partial)/(\partial x)(5x^2y^5)	\frac{\partial\:}{\partial\:x}(5x^{2}y^{5})
slope of-2x^2+50x+25.247	slope\:-2x^{2}+50x+25.247
derivative of sqrt(x^3+10)	\frac{d}{dx}(\sqrt{x^{3}+10})
integral of (ln(x+1))/((x+1)^3)	\int\:\frac{\ln(x+1)}{(x+1)^{3}}dx
y^'=(x+1)*(y+1)	y^{\prime\:}=(x+1)\cdot\:(y+1)
(x^2-1)(dy)/(dx)=x(y-1)	(x^{2}-1)\frac{dy}{dx}=x(y-1)
integral of 1/(2+x-x^2)	\int\:\frac{1}{2+x-x^{2}}dx
integral of (-2x)/(x^2+1)	\int\:\frac{-2x}{x^{2}+1}dx
limit as x approaches 0 of csc(x)-1/x	\lim\:_{x\to\:0}(\csc(x)-\frac{1}{x})
integral of-6x+5	\int\:-6x+5dx
integral of e^{-ax}x^2	\int\:e^{-ax}x^{2}dx
tangent of f(x)=3-e^{-3x},\at x=-ln(2)	tangent\:f(x)=3-e^{-3x},\at\:x=-\ln(2)
(\partial)/(\partial x)(20+5sin(x)cos(x-y))	\frac{\partial\:}{\partial\:x}(20+5\sin(x)\cos(x-y))
integral of (e^{2sqrt(x)})/(sqrt(x))	\int\:\frac{e^{2\sqrt{x}}}{\sqrt{x}}dx
derivative of 3/(x^2-1)	\frac{d}{dx}(\frac{3}{x^{2}-1})
integral of sin(3x)sin(7x)	\int\:\sin(3x)\sin(7x)dx
derivative of-x^{2/3}	\frac{d}{dx}(-x^{\frac{2}{3}})
limit as x approaches 1 of (x^3+1)/(x+1)	\lim\:_{x\to\:1}(\frac{x^{3}+1}{x+1})
y^'=(x^2+3x+2)/(y-2)	y^{\prime\:}=\frac{x^{2}+3x+2}{y-2}
derivative of arctan^2(x^3)	\frac{d}{dx}(\arctan^{2}(x^{3}))
(\partial)/(\partial y)(e^y*sin(x))	\frac{\partial\:}{\partial\:y}(e^{y}\cdot\:\sin(x))
tangent of f(x)= 1/(2sqrt(x+!))	tangent\:f(x)=\frac{1}{2\sqrt{x+!}}
laplacetransform-4t^2\delta(t-2)	laplacetransform\:-4t^{2}\delta(t-2)
area 4x^2,x^2+3	area\:4x^{2},x^{2}+3
y^'=(2x)/(y+x^2y)	y^{\prime\:}=\frac{2x}{y+x^{2}y}
integral from 1 to e of ln^2(x)	\int\:_{1}^{e}\ln^{2}(x)dx
integral of 1/8 x	\int\:\frac{1}{8}xdx
derivative of (sqrt(x))/(3(x^2+1))	derivative\:\frac{\sqrt{x}}{3(x^{2}+1)}
slope ofintercept (3,2),(6,8)	slopeintercept\:(3,2),(6,8)
integral of (sin(x/2))	\int\:(\sin(\frac{x}{2}))dx
area sin(x),3x, pi/2 ,pi	area\:\sin(x),3x,\frac{π}{2},π
limit as x approaches 1-of x/(x^2-1)	\lim\:_{x\to\:1-}(\frac{x}{x^{2}-1})
derivative of (x+2^{-2})	\frac{d}{dx}((x+2)^{-2})
derivative of 1/2 (6t^2+t)^{-3}	derivative\:\frac{1}{2}(6t^{2}+t)^{-3}
derivative of e^{3sin^2(2x})	\frac{d}{dx}(e^{3\sin^{2}(2x)})

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