What is the derivative of y= 4/((7x)^7) ?

The derivative of y= 4/((7x)^7) is -4/(117649x^8)

What is the first derivative of y= 4/((7x)^7) ?

The first derivative of y= 4/((7x)^7) is -4/(117649x^8)

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derivative of

y = \frac{4}{( 7 x ) ^{7}}

- \frac{4}{117649 x ^{8}}

Solution steps

\frac{d}{d x} (\frac{4}{( 7 x ) ^{7}})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{( 7 x ) ^{7}})

Apply exponent rule:

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

= 4 \frac{d}{d x} ((7 x)^{- 7})

Apply the chain rule:

- \frac{7}{( 7 x ) ^{8}} \frac{d}{d x} (7 x)

= - \frac{7}{( 7 x ) ^{8}} \frac{d}{d x} (7 x)

\frac{d}{d x} (7 x) = 7

= 4 (- \frac{7}{( 7 x ) ^{8}} \cdot 7)

Simplify

4 (- \frac{7}{( 7 x ) ^{8}} \cdot 7) : - \frac{4}{117649 x ^{8}}

= - \frac{4}{117649 x ^{8}}

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What is the derivative of y= 4/((7x)^7) ?
The derivative of y= 4/((7x)^7) is -4/(117649x^8)
What is the first derivative of y= 4/((7x)^7) ?
The first derivative of y= 4/((7x)^7) is -4/(117649x^8)