What is the derivative of (6x^{-5}) ?

The derivative of (6x^{-5}) is -5/(7776x^6)

What is the first derivative of (6x^{-5}) ?

The first derivative of (6x^{-5}) is -5/(7776x^6)

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\frac{d}{d x} ((6 x)^{- 5})

- \frac{5}{7776 x ^{6}}

Solution steps

\frac{d}{d x} ((6 x)^{- 5})

Apply the chain rule:

- \frac{5}{( 6 x ) ^{6}} \frac{d}{d x} (6 x)

= - \frac{5}{( 6 x ) ^{6}} \frac{d}{d x} (6 x)

\frac{d}{d x} (6 x) = 6

= - \frac{5}{( 6 x ) ^{6}} \cdot 6

Simplify

- \frac{5}{( 6 x ) ^{6}} \cdot 6 : - \frac{5}{7776 x ^{6}}

= - \frac{5}{7776 x ^{6}}

What is the derivative of (6x^{-5}) ?
The derivative of (6x^{-5}) is -5/(7776x^6)
What is the first derivative of (6x^{-5}) ?
The first derivative of (6x^{-5}) is -5/(7776x^6)