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Popular Calculus Problems

derivative of f(x)=(x^2+3)/x	derivative\:f(x)=\frac{x^{2}+3}{x}
(dy}{dx}(2y)+\frac{(1+y^2))/x =1	\frac{dy}{dx}(2y)+\frac{(1+y^{2})}{x}=1
(\partial)/(\partial t)(sin(x)cos(ct))	\frac{\partial\:}{\partial\:t}(\sin(x)\cos(ct))
integral of 18sin^2(x)cos^3(x)	\int\:18\sin^{2}(x)\cos^{3}(x)dx
derivative of arcsin(10x)	\frac{d}{dx}(\arcsin(10x))
integral from 2 to 3 of x+x^2	\int\:_{2}^{3}x+x^{2}dx
derivative of-(3x/(8-5x))	\frac{d}{dx}(-\frac{3x}{8-5x})
limit as n approaches infinity of (\sqrt[n]{n})/(ln(n))	\lim\:_{n\to\:\infty\:}(\frac{\sqrt[n]{n}}{\ln(n)})
limit as x approaches 4 of 4x+2x^2	\lim\:_{x\to\:4}(4x+2x^{2})
integral of cos^5(9-x)sin(9-x)	\int\:\cos^{5}(9-x)\sin(9-x)dx
integral of 1/(3x-x^2-2)	\int\:\frac{1}{3x-x^{2}-2}dx
integral of 3cot^5(θ)sin^4(θ)	\int\:3\cot^{5}(θ)\sin^{4}(θ)dθ
slope of x^2-2x+1	slope\:x^{2}-2x+1
derivative of \sqrt[3]{1-x^3+ln(x})	\frac{d}{dx}(\sqrt[3]{1-x^{3}+\ln(x)})
derivative of arctan(x-pi/2)	derivative\:\arctan(x-\frac{π}{2})
integral of x^3sqrt(x^2+35)	\int\:x^{3}\sqrt{x^{2}+35}dx
taylor e^{(x^3)}	taylor\:e^{(x^{3})}
area x^2,x=0,x=1	area\:x^{2},x=0,x=1
derivative of tan^2(sin^4(t))	derivative\:\tan^{2}(\sin^{4}(t))
inverse oflaplace 3/(s(s^2+8s+18))	inverselaplace\:\frac{3}{s(s^{2}+8s+18)}
limit as x approaches 2-of x^2-4	\lim\:_{x\to\:2-}(x^{2}-4)
integral from 1 to 5 of 2/(x^2+2x+1)	\int\:_{1}^{5}\frac{2}{x^{2}+2x+1}dx
integral of e^{-st}*(t^2-3t+1)	\int\:e^{-st}\cdot\:(t^{2}-3t+1)dt
derivative of ln(e^x+xe^x)	derivative\:\ln(e^{x}+xe^{x})
derivative of (3sqrt(x)+x(2-x^2))	\frac{d}{dx}((3\sqrt{x}+x)(2-x^{2}))
integral from 1 to 6 of 8x	\int\:_{1}^{6}8xdx
derivative of (5x)/(1+x^2)	derivative\:\frac{5x}{1+x^{2}}
(\partial)/(\partial x)(xy+x)	\frac{\partial\:}{\partial\:x}(xy+x)
derivative of-2sin(x+2sin(2x))	\frac{d}{dx}(-2\sin(x)+2\sin(2x))
integral of (cos(x)-sec(x))	\int\:(\cos(x)-\sec(x))dx
derivative of (t+5)^{2/3}(3t^2-2)^3	derivative\:(t+5)^{\frac{2}{3}}(3t^{2}-2)^{3}
(dy)/(dx)+5y=70,y(1)=110	\frac{dy}{dx}+5y=70,y(1)=110
limit as x approaches 10 of (7x^2-70x)/(x^2-100)	\lim\:_{x\to\:10}(\frac{7x^{2}-70x}{x^{2}-100})
integral of cos(0.5x)	\int\:\cos(0.5x)dx
taylor e^{-x/2}	taylor\:e^{-\frac{x}{2}}
derivative of te^t	derivative\:te^{t}
y^'-2y=x^2e^{2x}	y^{\prime\:}-2y=x^{2}e^{2x}
derivative of e^{5x-3}	\frac{d}{dx}(e^{5x-3})
integral of (1+x^2)^{1/2}	\int\:(1+x^{2})^{\frac{1}{2}}dx
integral of 2(sin(2x))^2	\int\:2(\sin(2x))^{2}dx
(\partial)/(\partial x)(xy*e^{xy})	\frac{\partial\:}{\partial\:x}(xy\cdot\:e^{xy})
derivative of 3x^2-e^x	\frac{d}{dx}(3x^{2}-e^{x})
integral of 4^tsin(4^t)	\int\:4^{t}\sin(4^{t})dt
derivative of sqrt(y-x+1)+sqrt(x-y+1)	\frac{d}{dx}(\sqrt{y-x+1}+\sqrt{x-y+1})
derivative of f(x)=ln(sqrt(x+9))	derivative\:f(x)=\ln(\sqrt{x+9})
derivative of-4ln(+1/x-4)	derivative\:-4\ln(+\frac{1}{x}-4)
(x^2+2y^2)dx=xydy	(x^{2}+2y^{2})dx=xydy
integral of (sin(1/(x^4)))/(x^5)	\int\:\frac{\sin(\frac{1}{x^{4}})}{x^{5}}dx
integral from 0.2 to 0.4 of 150x	\int\:_{0.2}^{0.4}150xdx
derivative of 5/(sqrt(x)+5)	derivative\:\frac{5}{\sqrt{x}+5}
y^'-(2x+1)y=0	y^{\prime\:}-(2x+1)y=0
integral of 1/(csc(x)(1+sin(x)))	\int\:\frac{1}{\csc(x)(1+\sin(x))}dx
integral from 0 to x of sqrt(1+36t)	\int\:_{0}^{x}\sqrt{1+36t}dt
integral from 1 to n of ln(x)	\int\:_{1}^{n}\ln(x)dx
derivative of (9+4x-6sqrt(x)/x)	\frac{d}{dx}(\frac{9+4x-6\sqrt{x}}{x})
(\partial)/(\partial x)(ln(x*cos(y)))	\frac{\partial\:}{\partial\:x}(\ln(x\cdot\:\cos(y)))
integral of 1/((x^2-441)^{3/2)}	\int\:\frac{1}{(x^{2}-441)^{\frac{3}{2}}}dx
derivative of \sqrt[3]{(3x^2+5x-1^2})	\frac{d}{dx}(\sqrt[3]{(3x^{2}+5x-1)^{2}})
y^{''}-2y^'+5y=e^{-2t}	y^{\prime\:\prime\:}-2y^{\prime\:}+5y=e^{-2t}
inverse oflaplace (2s-6)/(s^2+9)	inverselaplace\:\frac{2s-6}{s^{2}+9}
derivative of sin^4(2xcos^43x)	\frac{d}{dx}(\sin^{4}(2xco)s^{4}3x)
integral of 3xe^{(-2x)}	\int\:3xe^{(-2x)}dx
(\partial)/(\partial y)(sqrt(5x+4y))	\frac{\partial\:}{\partial\:y}(\sqrt{5x+4y})
derivative of 7/(sqrt(x+1))	\frac{d}{dx}(\frac{7}{\sqrt{x+1}})
integral from 1 to 5 of w^2ln(w)	\int\:_{1}^{5}w^{2}\ln(w)dw
integral of ({y})/(L{y\)}	\int\:\frac{\left\{y\right\}}{L\left\{y\right\}}dL
tangent of 5/((x^2+1))	tangent\:\frac{5}{(x^{2}+1)}
integral of 1+cos(2θ)	\int\:1+\cos(2θ)dθ
integral of (x^2-x-4)/(x^3+2x)	\int\:\frac{x^{2}-x-4}{x^{3}+2x}dx
integral of (x^3)/(sqrt((x+1)^2+4))	\int\:\frac{x^{3}}{\sqrt{(x+1)^{2}+4}}dx
derivative of 16^4sqrt(4x^4+4)	derivative\:16^{4}\sqrt{4x^{4}+4}
6y^'=x^2	6y^{\prime\:}=x^{2}
derivative of 1/3 x^3-x^2-8x+1	\frac{d}{dx}(\frac{1}{3}x^{3}-x^{2}-8x+1)
y^'=(2x^4+y^4)/(xy^3)	y^{\prime\:}=\frac{2x^{4}+y^{4}}{xy^{3}}
2x(dy)/(dx)=y^2	2x\frac{dy}{dx}=y^{2}
y^'=sqrt(9x+y)-9	y^{\prime\:}=\sqrt{9x+y}-9
integral of x/(x-6)	\int\:\frac{x}{x-6}dx
(\partial)/(\partial x)(2y-sin(x))	\frac{\partial\:}{\partial\:x}(2y-\sin(x))
derivative of x^3e^{4x}	\frac{d}{dx}(x^{3}e^{4x})
t^2y^{''}+7ty^'+5y=t	t^{2}y^{\prime\:\prime\:}+7ty^{\prime\:}+5y=t
derivative of 2/5 x^{15}	\frac{d}{dx}(\frac{2}{5}x^{15})
laplacetransform t^2cos(2t+30)	laplacetransform\:t^{2}\cos(2t+30^{\circ\:})
derivative of f(x)=5xsin(pix)	derivative\:f(x)=5x\sin(πx)
y^{''}-2y^'+y=e^xtan^{-1}(x)	y^{\prime\:\prime\:}-2y^{\prime\:}+y=e^{x}\tan^{-1}(x)
limit as x approaches-2 of [f(x)+g(x)]	\lim\:_{x\to\:-2}([f(x)+g(x)])
laplacetransform-5	laplacetransform\:-5
integral from 0 to 2pi of cos^3(θ)	\int\:_{0}^{2π}\cos^{3}(θ)dθ
derivative of (3x^2-4x+5/(6sqrt(x)))	\frac{d}{dx}(\frac{3x^{2}-4x+5}{6\sqrt{x}})
x(dy)/(dx)+y=9xy^2	x\frac{dy}{dx}+y=9xy^{2}
limit as x approaches 2+of 1/((x-2)^2)	\lim\:_{x\to\:2+}(\frac{1}{(x-2)^{2}})
(\partial)/(\partial x)(x/(x^2+81))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+81})
y^'-2y=3x^2	y^{\prime\:}-2y=3x^{2}
limit as x approaches 4 of x^2-16	\lim\:_{x\to\:4}(x^{2}-16)
limit as x approaches-2 of (5x+3)/(2x-9)	\lim\:_{x\to\:-2}(\frac{5x+3}{2x-9})
derivative of (2x^5-3)^8	derivative\:(2x^{5}-3)^{8}
integral from 0 to 2 of ((x+2))/((x-4))	\int\:_{0}^{2}\frac{(x+2)}{(x-4)}dx
(\partial)/(\partial x)(36-6x^2-y^2)	\frac{\partial\:}{\partial\:x}(36-6x^{2}-y^{2})
taylor (2x)/(sqrt(e^{2x^2)-1)}	taylor\:\frac{2x}{\sqrt{e^{2x^{2}}-1}}
derivative of 2sqrt(3)sin(x+2cos(x))	\frac{d}{dx}(2\sqrt{3}\sin(x)+2\cos(x))
integral from 1 to 2 of 3	\int\:_{1}^{2}3dx

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