What is the derivative of 1/((4x^3)) ?

The derivative of 1/((4x^3)) is -3/(64x^4)

What is the first derivative of 1/((4x^3)) ?

The first derivative of 1/((4x^3)) is -3/(64x^4)

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\frac{d}{d x} (\frac{1}{( 4 x ) ^{3}})

- \frac{3}{64 x ^{4}}

Solution steps

\frac{d}{d x} (\frac{1}{( 4 x ) ^{3}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 x) = 4

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

Simplify

- \frac{3}{( 4 x ) ^{4}} \cdot 4 : - \frac{3}{64 x ^{4}}

= - \frac{3}{64 x ^{4}}

What is the derivative of 1/((4x^3)) ?
The derivative of 1/((4x^3)) is -3/(64x^4)
What is the first derivative of 1/((4x^3)) ?
The first derivative of 1/((4x^3)) is -3/(64x^4)