What is the derivative of (3x^{-4}) ?

The derivative of (3x^{-4}) is -4/(81x^5)

What is the first derivative of (3x^{-4}) ?

The first derivative of (3x^{-4}) is -4/(81x^5)

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

- \frac{4}{81 x ^{5}}

Solution steps

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

Apply the chain rule:

- \frac{4}{( 3 x ) ^{5}} \frac{d}{d x} (3 x)

= - \frac{4}{( 3 x ) ^{5}} \frac{d}{d x} (3 x)

\frac{d}{d x} (3 x) = 3

= - \frac{4}{( 3 x ) ^{5}} \cdot 3

Simplify

- \frac{4}{( 3 x ) ^{5}} \cdot 3 : - \frac{4}{81 x ^{5}}

= - \frac{4}{81 x ^{5}}

What is the derivative of (3x^{-4}) ?
The derivative of (3x^{-4}) is -4/(81x^5)
What is the first derivative of (3x^{-4}) ?
The first derivative of (3x^{-4}) is -4/(81x^5)