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Popular Calculus Problems

derivative of e^xsin(e^x)	\frac{d}{dx}(e^{x}\sin(e^{x}))
derivative of x^2+xy	\frac{d}{dx}(x^{2}+xy)
d/(dt)(e^{3cos(t)+2t^2})	\frac{d}{dt}(e^{3\cos(t)+2t^{2}})
(\partial)/(\partial x)(e^{-9x^2-2y^2})	\frac{\partial\:}{\partial\:x}(e^{-9x^{2}-2y^{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})
integral from 2 to 7 of 3	\int\:_{2}^{7}3dx
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 of x^2(x^3+1)^{10}	\int\:x^{2}(x^{3}+1)^{10}dx
integral from pi/2 to pi of 4cot(x/2)	\int\:_{\frac{π}{2}}^{π}4\cot(\frac{x}{2})dx
derivative of 2x^3+x	\frac{d}{dx}(2x^{3}+x)
(\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}}
area cos(x),sin(2x),[0, pi/2 ]	area\:\cos(x),\sin(2x),[0,\frac{π}{2}]
(\partial)/(\partial u)(sqrt(u/v))	\frac{\partial\:}{\partial\:u}(\sqrt{\frac{u}{v}})
derivative of (x^2-1(-x^2-4x-2))	\frac{d}{dx}((x^{2}-1)(-x^{2}-4x-2))
(\partial)/(\partial x)(5x^2y^5)	\frac{\partial\:}{\partial\:x}(5x^{2}y^{5})
(\partial)/(\partial y)(xy^6+x^2+y^4)	\frac{\partial\:}{\partial\:y}(xy^{6}+x^{2}+y^{4})
(\partial)/(\partial z)(arctan(x/z))	\frac{\partial\:}{\partial\:z}(\arctan(\frac{x}{z}))
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)
limit as x approaches pi of tan(5/6 x)	\lim\:_{x\to\:π}(\tan(\frac{5}{6}x))
(x^2-1)(dy)/(dx)=x(y-1)	(x^{2}-1)\frac{dy}{dx}=x(y-1)
derivative of 7x^2+1	\frac{d}{dx}(7x^{2}+1)
integral of 1/(2+x-x^2)	\int\:\frac{1}{2+x-x^{2}}dx
integral of (4sin^3(sqrt(x)))/(sqrt(x))	\int\:\frac{4\sin^{3}(\sqrt{x})}{\sqrt{x}}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})
sum from n=0 to infinity of 5/(10^{3n)}	\sum\:_{n=0}^{\infty\:}\frac{5}{10^{3n}}
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
integral of (4sqrt(x)+\sqrt[4]{x})	\int\:(4\sqrt{x}+\sqrt[4]{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}
laplacetransform sin(5x)	laplacetransform\:\sin(5x)
integral from 1 to e of ln^2(x)	\int\:_{1}^{e}\ln^{2}(x)dx
limit as x approaches 5 of 5/(x-5)	\lim\:_{x\to\:5}(\frac{5}{x-5})
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)
derivative of sqrt(3)x+2cos(x)	derivative\:\sqrt{3}x+2\cos(x)
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})
f(x)=(sqrt(x))/(e^x)	f(x)=\frac{\sqrt{x}}{e^{x}}
tangent of y=8x-x^2(1.7)	tangent\:y=8x-x^{2}(1.7)
integral from 0 to 2 of 2pix(4-x^2)	\int\:_{0}^{2}2πx(4-x^{2})dx
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)})
(\partial)/(\partial x)(7e^xln(y))	\frac{\partial\:}{\partial\:x}(7e^{x}\ln(y))
derivative of sec^3(5x)	\frac{d}{dx}(\sec^{3}(5x))
derivative of arctan(6x)	derivative\:\arctan(6x)
tangent of f(x)=x^3+2x^2+4	tangent\:f(x)=x^{3}+2x^{2}+4
derivative of 18	\frac{d}{dx}(18)
f(x)=(2-xcos(pix))/(x-2)	f(x)=\frac{2-x\cos(πx)}{x-2}
area y=3x,y= 3/5 x,y=28-x^2	area\:y=3x,y=\frac{3}{5}x,y=28-x^{2}
(\partial)/(\partial x)(x^5e^{3xy})	\frac{\partial\:}{\partial\:x}(x^{5}e^{3xy})
(\partial)/(\partial y)(2+ye^{xy})	\frac{\partial\:}{\partial\:y}(2+ye^{xy})
integral of 1/(4+(x-2)^2)	\int\:\frac{1}{4+(x-2)^{2}}dx
(dy)/(dt)=ky^2,y(0)=47	\frac{dy}{dt}=ky^{2},y(0)=47
(\partial)/(\partial x)((x^2+y^2)^{3/2})	\frac{\partial\:}{\partial\:x}((x^{2}+y^{2})^{\frac{3}{2}})
(\partial)/(\partial x)(x^3-y^3+2xy)	\frac{\partial\:}{\partial\:x}(x^{3}-y^{3}+2xy)
limit as x approaches 2 of sqrt(3x-6)	\lim\:_{x\to\:2}(\sqrt{3x-6})
(\partial)/(\partial x)(e(y^2))	\frac{\partial\:}{\partial\:x}(e(y^{2}))
derivative of f(x)=sin^3(2x)	derivative\:f(x)=\sin^{3}(2x)
derivative of y=8x^3-5x^2-x/(12)	derivative\:y=8x^{3}-5x^{2}-\frac{x}{12}
derivative of (x^5+5)^{4/3}tan(2x)	derivative\:(x^{5}+5)^{\frac{4}{3}}\tan(2x)
derivative of arctan(x/(1-x))	derivative\:\arctan(\frac{x}{1-x})
derivative of x^{0.45}	\frac{d}{dx}(x^{0.45})
(\partial)/(\partial x)(ln(x^4+y^4))	\frac{\partial\:}{\partial\:x}(\ln(x^{4}+y^{4}))
integral of e^tsin(2t)	\int\:e^{t}\sin(2t)dt
slope of y=6+5x^2-2x^3	slope\:y=6+5x^{2}-2x^{3}
derivative of cos^7(2x^2+1)	\frac{d}{dx}(\cos^{7}(2x^{2}+1))
derivative of ((x+3/(x-3))^5)	\frac{d}{dx}((\frac{x+3}{x-3})^{5})

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