What is the derivative of 4x^{-3}+6x^{-8/3} ?

The derivative of 4x^{-3}+6x^{-8/3} is (-12x^{11/3}-16x^4)/(x^{23/3)}

What is the first derivative of 4x^{-3}+6x^{-8/3} ?

The first derivative of 4x^{-3}+6x^{-8/3} is (-12x^{11/3}-16x^4)/(x^{23/3)}

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derivative of

4 x^{- 3} + 6 x^{- \frac{8}{3}}

\frac{- 12 x ^{\frac{11}{3}} - 16 x ^{4}}{x ^{\frac{23}{3}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 x^{- 3}) + \frac{d}{d x} (6 x^{- \frac{8}{3}})

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

\frac{d}{d x} (6 x^{- \frac{8}{3}}) = - \frac{16}{x ^{\frac{11}{3}}}

= - \frac{12}{x ^{4}} - \frac{16}{x ^{\frac{11}{3}}}

Simplify

- \frac{12}{x ^{4}} - \frac{16}{x ^{\frac{11}{3}}} : \frac{- 12 x ^{\frac{11}{3}} - 16 x ^{4}}{x ^{\frac{23}{3}}}

= \frac{- 12 x ^{\frac{11}{3}} - 16 x ^{4}}{x ^{\frac{23}{3}}}

\frac{\partial}{\partial x} (arcsin (3 x + y))

f (x) = 6 e^{x} cos (x)

y^{2} = x + 2, y^{2} = 2 - x

f (x) = - \frac{7}{( x - 7 ) ^{2}}

\int sin^{2} (\frac{2 π x}{L}) d x

What is the derivative of 4x^{-3}+6x^{-8/3} ?
The derivative of 4x^{-3}+6x^{-8/3} is (-12x^{11/3}-16x^4)/(x^{23/3)}
What is the first derivative of 4x^{-3}+6x^{-8/3} ?
The first derivative of 4x^{-3}+6x^{-8/3} is (-12x^{11/3}-16x^4)/(x^{23/3)}