What is the derivative of \sqrt[5]{ln(6-x^2}) ?

The derivative of \sqrt[5]{ln(6-x^2}) is -(2x)/(5ln^{4/5)(6-x^2)(6-x^2)}

What is the first derivative of \sqrt[5]{ln(6-x^2}) ?

The first derivative of \sqrt[5]{ln(6-x^2}) is -(2x)/(5ln^{4/5)(6-x^2)(6-x^2)}

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العربية

- \frac{2 x}{5 ln ^{\frac{4}{5}} ( 6 - x ^{2} ) ( 6 - x ^{2} )}

Solution steps

Apply the chain rule:

\frac{1}{5 ( ln ( 6 - x ^{2} ) ) ^{\frac{4}{5}}} \frac{d}{d x} (ln (6 - x^{2}))

= \frac{1}{5 ( ln ( 6 - x ^{2} ) ) ^{\frac{4}{5}}} \frac{d}{d x} (ln (6 - x^{2}))

\frac{d}{d x} (ln (6 - x^{2})) = - \frac{2 x}{6 - x ^{2}}

= \frac{1}{5 ( ln ( 6 - x ^{2} ) ) ^{\frac{4}{5}}} (- \frac{2 x}{6 - x ^{2}})

Simplify

\frac{1}{5 ln ^{\frac{4}{5}} ( 6 - x ^{2} )} (- \frac{2 x}{6 - x ^{2}}) : - \frac{2 x}{5 ln ^{\frac{4}{5}} ( 6 - x ^{2} ) ( 6 - x ^{2} )}

= - \frac{2 x}{5 ln ^{\frac{4}{5}} ( 6 - x ^{2} ) ( 6 - x ^{2} )}

What is the derivative of \sqrt[5]{ln(6-x^2}) ?
The derivative of \sqrt[5]{ln(6-x^2}) is -(2x)/(5ln^{4/5)(6-x^2)(6-x^2)}
What is the first derivative of \sqrt[5]{ln(6-x^2}) ?
The first derivative of \sqrt[5]{ln(6-x^2}) is -(2x)/(5ln^{4/5)(6-x^2)(6-x^2)}