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Popular >

derivative of (x^3/(12)+2/3 x^{-3})

Solution

\frac{d}{d x} (\frac{x ^{3}}{12} + \frac{2}{3} x^{- 3})

Solution

\frac{x ^{2}}{4} - \frac{2}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{x ^{3}}{12} + \frac{2}{3} x^{- 3})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x ^{3}}{12}) + \frac{d}{d x} (\frac{2}{3} x^{- 3})

\frac{d}{d x} (\frac{x ^{3}}{12}) = \frac{x ^{2}}{4}

\frac{d}{d x} (\frac{2}{3} x^{- 3}) = - \frac{2}{x ^{4}}

= \frac{x ^{2}}{4} - \frac{2}{x ^{4}}

Graph

Popular Examples

derivative of-8e^{-x/(10}-40)

\frac{d}{d x} (- 8 e^{- \frac{x}{10}} - 40)

integral from 0 to 8 of 4/((x-6)^3)

\int_{0}^{8} \frac{4}{( x - 6 ) ^{3}} d x

tangent of f(x)=(1+2x)^{10},(0,1)tangent of

f (x) = (1 + 2 x)^{10}, (0, 1)

(\partial)/(\partial x)((3xy^2)/(x^2+y^4))

\frac{\partial}{\partial x} (\frac{3 x y ^{2}}{x ^{2} + y ^{4}})

integral of 5xe^{4x}

\int 5 x e^{4 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^3/(12)+2/3 x^{-3}) ?
The derivative of (x^3/(12)+2/3 x^{-3}) is (x^2)/4-2/(x^4)
What is the first derivative of (x^3/(12)+2/3 x^{-3}) ?
The first derivative of (x^3/(12)+2/3 x^{-3}) is (x^2)/4-2/(x^4)