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Popular Calculus Problems

area 9/x ,2x, 1/2 x	area\:\frac{9}{x},2x,\frac{1}{2}x
integral of 4(cos(x)+sin(2x))/(sin(x))	\int\:4\frac{\cos(x)+\sin(2x)}{\sin(x)}dx
derivative of y=cos^2(1-3x^2)	derivative\:y=\cos^{2}(1-3x^{2})
limit as x approaches 0-of e^{6/x}	\lim\:_{x\to\:0-}(e^{\frac{6}{x}})
limit as x approaches-1+of arccos(x)	\lim\:_{x\to\:-1+}(\arccos(x))
2y+(x+1)(dy)/(dx)=3x+3	2y+(x+1)\frac{dy}{dx}=3x+3
derivative of (480t)/((t^2+5)^3)	derivative\:\frac{480t}{(t^{2}+5)^{3}}
integral of 5e^{-0.1x}	\int\:5e^{-0.1x}dx
limit as x approaches 1 of-3x+5	\lim\:_{x\to\:1}(-3x+5)
t(dy)/(dt)+(t+1)y=2te^{-t}	t\frac{dy}{dt}+(t+1)y=2te^{-t}
tangent of 3x^2+4x-2	tangent\:3x^{2}+4x-2
tangent of y= 3/(sqrt(x)),\at x= 1/16	tangent\:y=\frac{3}{\sqrt{x}},\at\:x=\frac{1}{16}
(x^2+1)y^'=xy	(x^{2}+1)y^{\prime\:}=xy
derivative of ln(tan(x+sec(x)))	\frac{d}{dx}(\ln(\tan(x)+\sec(x)))
integral of cos^2(2u)	\int\:\cos^{2}(2u)du
integral of x^3-6x^2+8x	\int\:x^{3}-6x^{2}+8xdx
limit as x approaches 0 of e^{3x}-1	\lim\:_{x\to\:0}(e^{3x}-1)
integral of 4xe^{-2x}	\int\:4xe^{-2x}dx
integral of x\sqrt[5]{(x+1)^2}	\int\:x\sqrt[5]{(x+1)^{2}}dx
(x^2-25ln(x^2))^'	(x^{2}-25\ln(x^{2}))^{\prime\:}
integral of (10)/(15sin(x)-8cos(x))	\int\:\frac{10}{15\sin(x)-8\cos(x)}dx
integral of 6/(xsqrt(36-(ln(x))^2))	\int\:\frac{6}{x\sqrt{36-(\ln(x))^{2}}}dx
tangent of f(x)=6xcos(x),(pi,-6pi)	tangent\:f(x)=6x\cos(x),(π,-6π)
derivative of e^{2x}-e^{-2x}-4x	\frac{d}{dx}(e^{2x}-e^{-2x}-4x)
derivative of 3/(sqrt(x+9))	derivative\:\frac{3}{\sqrt{x+9}}
y*y^'=(5x)/(4sqrt(x^2+1))	y\cdot\:y^{\prime\:}=\frac{5x}{4\sqrt{x^{2}+1}}
derivative of x/(x^2+9)	derivative\:\frac{x}{x^{2}+9}
integral of 1/(z^3sqrt(z^2-81))	\int\:\frac{1}{z^{3}\sqrt{z^{2}-81}}dz
(\partial)/(\partial x)(6y^8x^5-5y^7x^4)	\frac{\partial\:}{\partial\:x}(6y^{8}x^{5}-5y^{7}x^{4})
integral of ((x+2))/(sqrt(x^2+4))	\int\:\frac{(x+2)}{\sqrt{x^{2}+4}}dx
integral of 1/(3cos(u)-5-4sin(u))	\int\:\frac{1}{3\cos(u)-5-4\sin(u)}du
derivative of \sqrt[4]{xy}	\frac{d}{dx}(\sqrt[4]{xy})
derivative of x^{4pi}	\frac{d}{dx}(x^{4π})
(\partial)/(\partial x)(y^{1/3}x^3)	\frac{\partial\:}{\partial\:x}(y^{\frac{1}{3}}x^{3})
d/(dv)(u/v)	\frac{d}{dv}(\frac{u}{v})
integral from 0 to 1 of-2(x^2+1)e^{-x}	\int\:_{0}^{1}-2(x^{2}+1)e^{-x}dx
derivative of f(x)=arcsec(2x)	derivative\:f(x)=\arcsec(2x)
laplacetransform 5t-3	laplacetransform\:5t-3
(\partial)/(\partial x)((x+y)^8)	\frac{\partial\:}{\partial\:x}((x+y)^{8})
derivative of sqrt(r^2-6x^2)	derivative\:\sqrt{r^{2}-6x^{2}}
tangent of f(x)=x^4-13x^2+36,\at x=2	tangent\:f(x)=x^{4}-13x^{2}+36,\at\:x=2
integral of-4x^3e^{4x^2}	\int\:-4x^{3}e^{4x^{2}}dx
y^'+y=y^{-2}	y^{\prime\:}+y=y^{-2}
integral of e^{3t}(e^{3t}-1)	\int\:e^{3t}(e^{3t}-1)dt
inverse oflaplace ((s+1))/((s+1)^2+1)	inverselaplace\:\frac{(s+1)}{(s+1)^{2}+1}
slope of (-1,6),(7,-2)	slope\:(-1,6),(7,-2)
(dy)/(dx)=y-x	\frac{dy}{dx}=y-x
derivative of F(C)= 9/5 C+32	derivative\:F(C)=\frac{9}{5}C+32
(2x-3y)dx+(2y-3x)dy=0	(2x-3y)dx+(2y-3x)dy=0
derivative of \|x^2\|	\frac{d}{dx}(\left\|x^{2}\right\|)
taylor 1/(4-x)	taylor\:\frac{1}{4-x}
derivative of sqrt(4x-1)	derivative\:\sqrt{4x-1}
y^'=((x-8))/x	y^{\prime\:}=\frac{(x-8)}{x}
(\partial)/(\partial x)(U(x)(1+(R(x)^3)/(x^3)))	\frac{\partial\:}{\partial\:x}(U(x)(1+\frac{R(x)^{3}}{x^{3}}))
area 2x+y^2=48,x=y	area\:2x+y^{2}=48,x=y
y^'+3y=4sin(e^{3x})	y^{\prime\:}+3y=4\sin(e^{3x})
integral of (13)/(sqrt(25-9x^2))	\int\:\frac{13}{\sqrt{25-9x^{2}}}dx
derivative of ((2x^2+3x))/(4x^2)	derivative\:\frac{(2x^{2}+3x)}{4x^{2}}
derivative of axsin(2x+bxcos(2x))	\frac{d}{dx}(ax\sin(2x)+bx\cos(2x))
(dx}{dt}=-\frac{50)/pi x^{-3/2}	\frac{dx}{dt}=-\frac{50}{π}x^{-\frac{3}{2}}
integral of (sin(x)-2e^x+3sqrt(x))	\int\:(\sin(x)-2e^{x}+3\sqrt{x})dx
integral of y^2(1/(y^5)+(y^4)/2)	\int\:y^{2}(\frac{1}{y^{5}}+\frac{y^{4}}{2})dy
derivative of 6xarcsin(x)	derivative\:6x\arcsin(x)
derivative of (t+e^t)(9-sqrt(t))	derivative\:(t+e^{t})(9-\sqrt{t})
3y^{'''}+12y^{''}+12y^'=0	3y^{\prime\:\prime\:\prime\:}+12y^{\prime\:\prime\:}+12y^{\prime\:}=0
integral from 0 to 1 of (x^2+x)e^x	\int\:_{0}^{1}(x^{2}+x)e^{x}dx
integral from 0 to 1 of e^{-t^2}	\int\:_{0}^{1}e^{-t^{2}}dt
(d^2y)/(dx^2)-6(dy)/(dx)+8y=0	\frac{d^{2}y}{dx^{2}}-6\frac{dy}{dx}+8y=0
derivative of sec^2(2x+5)*2	derivative\:\sec^{2}(2x+5)\cdot\:2
limit as n approaches 2 of n^2	\lim\:_{n\to\:2}(n^{2})
derivative of f(x)=(5x-5)(2x^3-x^2+1)	derivative\:f(x)=(5x-5)(2x^{3}-x^{2}+1)
(\partial)/(\partial u)(sqrt(u^5+v^9))	\frac{\partial\:}{\partial\:u}(\sqrt{u^{5}+v^{9}})
integral from 1 to e^4 of (ln^3(x^2))/x	\int\:_{1}^{e^{4}}\frac{\ln^{3}(x^{2})}{x}dx
derivative of x^{4/3}+4x^{1/3}	\frac{d}{dx}(x^{\frac{4}{3}}+4x^{\frac{1}{3}})
(\partial)/(\partial x)(sin(x^4+y^3))	\frac{\partial\:}{\partial\:x}(\sin(x^{4}+y^{3}))
tangent of f(x)=x^2-3,(4,13)	tangent\:f(x)=x^{2}-3,(4,13)
limit as x approaches 0+of 7/x-7/(\|x\|)	\lim\:_{x\to\:0+}(\frac{7}{x}-\frac{7}{\left\|x\right\|})
derivative of 2/(1+x^3)	\frac{d}{dx}(\frac{2}{1+x^{3}})
inverse oflaplace (s^2)/((s-3)^2)	inverselaplace\:\frac{s^{2}}{(s-3)^{2}}
slope of 2+5x^2-2x^3	slope\:2+5x^{2}-2x^{3}
tangent of f(x)=x^2-7x+7,\at x=6	tangent\:f(x)=x^{2}-7x+7,\at\:x=6
tangent of f(x)=(6-3x)(6+3x),\at x=3	tangent\:f(x)=(6-3x)(6+3x),\at\:x=3
integral from-0.5 to 0.5 of 1.5x^2	\int\:_{-0.5}^{0.5}1.5x^{2}dx
derivative of y=(3x-2)^2(5x+4)	derivative\:y=(3x-2)^{2}(5x+4)
inverse oflaplace (-1)/(s^2-1)	inverselaplace\:\frac{-1}{s^{2}-1}
derivative of 2/x+sqrt(x)	\frac{d}{dx}(\frac{2}{x}+\sqrt{x})
(\partial)/(\partial v)(1/(u^2+v^2))	\frac{\partial\:}{\partial\:v}(\frac{1}{u^{2}+v^{2}})
integral of (7+6x)/(1+x^2)	\int\:\frac{7+6x}{1+x^{2}}dx
limit as x approaches 3 of 2x-5	\lim\:_{x\to\:3}(2x-5)
limit as x approaches pi/x of xcos(x)	\lim\:_{x\to\:\frac{π}{x}}(x\cos(x))
limit as x approaches-2 of \sqrt[3]{x+2}	\lim\:_{x\to\:-2}(\sqrt[3]{x+2})
tangent of y=(5x)/(x+2)(3.3)	tangent\:y=\frac{5x}{x+2}(3.3)
(dy)/(dx)=-(x+6)/(7y^2)	\frac{dy}{dx}=-\frac{x+6}{7y^{2}}
limit as x approaches-pi/3 of sec(x)	\lim\:_{x\to\:-\frac{π}{3}}(\sec(x))
(\partial)/(\partial x)(-arctan(y/x))	\frac{\partial\:}{\partial\:x}(-\arctan(\frac{y}{x}))
4x^2+5y(dy)/(dx)=0	4x^{2}+5y\frac{dy}{dx}=0
x^{''}+x^'-2x=e^t	x^{\prime\:\prime\:}+x^{\prime\:}-2x=e^{t}
integral from 0 to 4 of pix^2	\int\:_{0}^{4}πx^{2}dx
derivative of-5e^{-x/3}+2	derivative\:-5e^{-\frac{x}{3}}+2
limit as x approaches-4 of (x-4)/(x-8)	\lim\:_{x\to\:-4}(\frac{x-4}{x-8})

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