What is the derivative of y= 5/((2x)^3) ?

The derivative of y= 5/((2x)^3) is -(15)/(8x^4)

What is the first derivative of y= 5/((2x)^3) ?

The first derivative of y= 5/((2x)^3) is -(15)/(8x^4)

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derivative of

y = \frac{5}{( 2 x ) ^{3}}

- \frac{15}{8 x ^{4}}

Solution steps

\frac{d}{d x} (\frac{5}{( 2 x ) ^{3}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (\frac{1}{( 2 x ) ^{3}})

Apply exponent rule:

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

= 5 \frac{d}{d x} ((2 x)^{- 3})

Apply the chain rule:

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

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

\frac{d}{d x} (2 x) = 2

= 5 (- \frac{3}{( 2 x ) ^{4}} \cdot 2)

Simplify

5 (- \frac{3}{( 2 x ) ^{4}} \cdot 2) : - \frac{15}{8 x ^{4}}

= - \frac{15}{8 x ^{4}}

What is the derivative of y= 5/((2x)^3) ?
The derivative of y= 5/((2x)^3) is -(15)/(8x^4)
What is the first derivative of y= 5/((2x)^3) ?
The first derivative of y= 5/((2x)^3) is -(15)/(8x^4)