What is the derivative of ln((6-7x^4^6)) ?

The derivative of ln((6-7x^4^6)) is -(168x^3)/(6-7x^4)

What is the first derivative of ln((6-7x^4^6)) ?

The first derivative of ln((6-7x^4^6)) is -(168x^3)/(6-7x^4)

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\frac{d}{d x} (ln ((6 - 7 x^{4})^{6}))

- \frac{168 x ^{3}}{6 - 7 x ^{4}}

Solution steps

\frac{d}{d x} (ln ((6 - 7 x^{4})^{6}))

Apply the chain rule:

\frac{1}{( 6 - 7 x ^{4} ) ^{6}} \frac{d}{d x} ((6 - 7 x^{4})^{6})

= \frac{1}{( 6 - 7 x ^{4} ) ^{6}} \frac{d}{d x} ((6 - 7 x^{4})^{6})

\frac{d}{d x} ((6 - 7 x^{4})^{6}) = - 168 x^{3} (6 - 7 x^{4})^{5}

= \frac{1}{( 6 - 7 x ^{4} ) ^{6}} (- 168 x^{3} (6 - 7 x^{4})^{5})

Simplify

\frac{1}{( 6 - 7 x ^{4} ) ^{6}} (- 168 x^{3} (6 - 7 x^{4})^{5}) : - \frac{168 x ^{3}}{6 - 7 x ^{4}}

= - \frac{168 x ^{3}}{6 - 7 x ^{4}}

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What is the derivative of ln((6-7x^4^6)) ?
The derivative of ln((6-7x^4^6)) is -(168x^3)/(6-7x^4)
What is the first derivative of ln((6-7x^4^6)) ?
The first derivative of ln((6-7x^4^6)) is -(168x^3)/(6-7x^4)