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Popular Calculus Problems

tangent of f(x)= 8/(x+3),2	tangent\:f(x)=\frac{8}{x+3},2
limit as x approaches 3+of sqrt(9-x^2)	\lim\:_{x\to\:3+}(\sqrt{9-x^{2}})
taylor 1/(x+5),0	taylor\:\frac{1}{x+5},0
integral from 0 to 5 of \|5x-1\|	\int\:_{0}^{5}\left\|5x-1\right\|dx
integral from 1 to 3 of (2x)	\int\:_{1}^{3}(2x)dx
(dy)/(dx)=a-by	\frac{dy}{dx}=a-by
f(x)=ln(sin^2(x))	f(x)=\ln(\sin^{2}(x))
f^'(x)=-2x+8	f^{\prime\:}(x)=-2x+8
xy^{''}-y^'=0	xy^{\prime\:\prime\:}-y^{\prime\:}=0
integral of (4x^2-3x)^4(8x-3)	\int\:(4x^{2}-3x)^{4}(8x-3)dx
d/(dt)(t+sin(t))	\frac{d}{dt}(t+\sin(t))
integral of 1/5 e^{5x}	\int\:\frac{1}{5}e^{5x}dx
sum from n=1 to infinity of 4(3/2)^{n-1}	\sum\:_{n=1}^{\infty\:}4(\frac{3}{2})^{n-1}
(dy)/(dx)=(y(x-y))/(x^2)	\frac{dy}{dx}=\frac{y(x-y)}{x^{2}}
derivative of sin(xcos(x)1/x)	\frac{d}{dx}(\sin(x)\cdot\:\cos(x)\cdot\:\frac{1}{x})
area y=6x^2,y=4x^2,y=6-5x	area\:y=6x^{2},y=4x^{2},y=6-5x
derivative of 2cos(x+2)	\frac{d}{dx}(2\cos(x)+2)
d/(dt)(e^{8t})	\frac{d}{dt}(e^{8t})
derivative of-1/(x^2-2/(x^3))	\frac{d}{dx}(-\frac{1}{x^{2}}-\frac{2}{x^{3}})
(\partial)/(\partial x)(e^{xy^2}-2ln(x)+3y)	\frac{\partial\:}{\partial\:x}(e^{xy^{2}}-2\ln(x)+3y)
f(x)=2xsin(3x)	f(x)=2x\sin(3x)
limit as x approaches 2 of 3x-4	\lim\:_{x\to\:2}(3x-4)
derivative of 3sqrt(x)ln(x)	\frac{d}{dx}(3\sqrt{x}\ln(x))
derivative of (1-x^2)	\frac{d}{dx}((1-x)^{2})
derivative of f(x)=(4x+x^2)/((2+x)^2)	derivative\:f(x)=\frac{4x+x^{2}}{(2+x)^{2}}
integral from 0 to 3 of sqrt(17)	\int\:_{0}^{3}\sqrt{17}dx
6y^{''}+6y^'-12y=0	6y^{\prime\:\prime\:}+6y^{\prime\:}-12y=0
derivative of y=2x^3+3x^2-12x+7	derivative\:y=2x^{3}+3x^{2}-12x+7
integral of (12x)/(sqrt(1+4x))	\int\:\frac{12x}{\sqrt{1+4x}}dx
derivative of (x^3/3+x^2+4x-10)	\frac{d}{dx}(\frac{x^{3}}{3}+x^{2}+4x-10)
integral of sin(2pi)	\int\:\sin(2π)
limit as x approaches 1-of (x+1)/(1-x)	\lim\:_{x\to\:1-}(\frac{x+1}{1-x})
(\partial)/(\partial x)(sqrt(x)y)	\frac{\partial\:}{\partial\:x}(\sqrt{x}y)
derivative of ln(0)	\frac{d}{dx}(\ln(0))
(\partial}{\partial x}(\frac{e^x)/x)	\frac{\partial\:}{\partial\:x}(\frac{e^{x}}{x})
derivative of xln(2x+1)	\frac{d}{dx}(x\ln(2x+1))
derivative of 1/3 cos(3x)	\frac{d}{dx}(\frac{1}{3}\cos(3x))
derivative of (2x-4^4(x^2+x+1)^5)	\frac{d}{dx}((2x-4)^{4}(x^{2}+x+1)^{5})
area x^2(x-4),[-1,5]	area\:x^{2}(x-4),[-1,5]
integral of ((5x+3))/((x^2+4x+7))	\int\:\frac{(5x+3)}{(x^{2}+4x+7)}dx
derivative of (5x-1^2)	\frac{d}{dx}((5x-1)^{2})
sum from k=1 to infinity of k/(k^2+1)	\sum\:_{k=1}^{\infty\:}\frac{k}{k^{2}+1}
integral from 0 to 1-y of 6x	\int\:_{0}^{1-y}6xdx
(\partial)/(\partial x)(3(((4+x))/(5+z))^2)	\frac{\partial\:}{\partial\:x}(3(\frac{(4+x)}{5+z})^{2})
integral of (sin(x)+sinh(x))	\int\:(\sin(x)+\sinh(x))dx
inverse oflaplace (3s+12)/(s(s^2+4))	inverselaplace\:\frac{3s+12}{s(s^{2}+4)}
integral of 1/((x^2-9)^{3/2)}	\int\:\frac{1}{(x^{2}-9)^{\frac{3}{2}}}dx
(\partial)/(\partial x)(1/(e^x-1))	\frac{\partial\:}{\partial\:x}(\frac{1}{e^{x}-1})
f(x)=e^x*x	f(x)=e^{x}\cdot\:x
derivative of x^{y^x}	\frac{d}{dx}(x^{y^{x}})
integral of 3/(x^2+4)	\int\:\frac{3}{x^{2}+4}dx
integral of x^4sqrt(x^5+3)	\int\:x^{4}\sqrt{x^{5}+3}dx
(\partial)/(\partial y)(2e^{x/2+y}-y)	\frac{\partial\:}{\partial\:y}(2e^{\frac{x}{2}+y}-y)
derivative of (490t)/((t^2+7)^3)	derivative\:\frac{490t}{(t^{2}+7)^{3}}
derivative of (x^2(x+2^4)/((2x^2-1)^3))	\frac{d}{dx}(\frac{x^{2}(x+2)^{4}}{(2x^{2}-1)^{3}})
laplacetransform sin(t-8)	laplacetransform\:\sin(t-8)
(\partial)/(\partial x)(ye^{xz})	\frac{\partial\:}{\partial\:x}(ye^{xz})
derivative of 6x^2sin(xtan(x))	\frac{d}{dx}(6x^{2}\sin(x)\tan(x))
integral of sqrt(1+(e^x)^2)	\int\:\sqrt{1+(e^{x})^{2}}dx
integral of 3*e^{-3y+6}	\int\:3\cdot\:e^{-3y+6}dy
derivative of (1-2ln(x)/(x^3))	\frac{d}{dx}(\frac{1-2\ln(x)}{x^{3}})
derivative of in^2x	\frac{d}{dx}(in^{2}x)
limit as x approaches 6 of 9/(9-(-1))	\lim\:_{x\to\:6}(\frac{9}{9-(-1)})
integral of tan^2(θ)sec^2(θ)	\int\:\tan^{2}(θ)\sec^{2}(θ)dθ
(\partial)/(\partial x)(sin(2x+y)sin(y))	\frac{\partial\:}{\partial\:x}(\sin(2x+y)\sin(y))
integral of tan^3(x)sec^{2n+1}(x)	\int\:\tan^{3}(x)\sec^{2n+1}(x)dx
integral of x^3-1	\int\:x^{3}-1dx
integral of (x+3)(x^2+6x+7)^6	\int\:(x+3)(x^{2}+6x+7)^{6}dx
derivative of f(x)=2x^4-16x^2+6	derivative\:f(x)=2x^{4}-16x^{2}+6
integral of (3cos(x)-e^x+5/x)	\int\:(3\cos(x)-e^{x}+\frac{5}{x})dx
(dy)/(dx)=0.4^{x/3}	\frac{dy}{dx}=0.4^{\frac{x}{3}}
3y^{''}+5y^'=0	3y^{\prime\:\prime\:}+5y^{\prime\:}=0
(\partial)/(\partial y)(xy^8+x^2+y^4)	\frac{\partial\:}{\partial\:y}(xy^{8}+x^{2}+y^{4})
integral of (sin(9ln(t)))/t	\int\:\frac{\sin(9\ln(t))}{t}dt
sum from n=1 to infinity of arctan(6n)	\sum\:_{n=1}^{\infty\:}\arctan(6n)
integral of x^2x	\int\:x^{2}xdx
d/(dt)(e^{(7tsin(2t))})	\frac{d}{dt}(e^{(7t\sin(2t))})
laplacetransform e^{,\at}	laplacetransform\:e^{,\at\:}
y^'=2y-t	y^{\prime\:}=2y-t
f(x)=(ln(x))/(x^9)	f(x)=\frac{\ln(x)}{x^{9}}
derivative of (6x^2+1/(x^2+8))	\frac{d}{dx}(\frac{6x^{2}+1}{x^{2}+8})
derivative of y=cos((pix)^8)	derivative\:y=\cos((πx)^{8})
integral from-1 to 2 of x^2(x^3+1)^2	\int\:_{-1}^{2}x^{2}(x^{3}+1)^{2}dx
(dy)/(dx)=100x(y+2)	\frac{dy}{dx}=100x(y+2)
tangent of y=3e^xcos(x),(0,3)	tangent\:y=3e^{x}\cos(x),(0,3)
4y^{''}+12y^'+9y=0	4y^{\prime\:\prime\:}+12y^{\prime\:}+9y=0
y^'= y/x+2x+1	y^{\prime\:}=\frac{y}{x}+2x+1
derivative of f(x)= 1/2 x^8	derivative\:f(x)=\frac{1}{2}x^{8}
(\partial)/(\partial x)(ye^x+xe^y)	\frac{\partial\:}{\partial\:x}(ye^{x}+xe^{y})
derivative of sqrt(t)	derivative\:\sqrt{t}
slope of (1.5)(2.8)	slope\:(1.5)(2.8)
integral from 1 to 6 of (x^2+3)/(7x-x^2)	\int\:_{1}^{6}\frac{x^{2}+3}{7x-x^{2}}dx
integral from pi/6 to pi of sin(x)	\int\:_{\frac{π}{6}}^{π}\sin(x)dx
derivative of-8/((1+4x)^2)	derivative\:-\frac{8}{(1+4x)^{2}}
integral of 1/2+1/2 cos(2x)	\int\:\frac{1}{2}+\frac{1}{2}\cos(2x)dx
integral from 1 to 2 of (x^4+1/(4x^4))	\int\:_{1}^{2}(x^{4}+\frac{1}{4x^{4}})dx
derivative of x^4-2x^4	derivative\:x^{4}-2x^{4}
integral of x/(x^2+x-2)	\int\:\frac{x}{x^{2}+x-2}dx
integral of-3xe^{-3x}	\int\:-3xe^{-3x}dx
sum from x=0 to infinity of x/(5^x)	\sum\:_{x=0}^{\infty\:}\frac{x}{5^{x}}

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