What is the derivative of \sqrt[3]{ln(4-x^2)} ?

The derivative of \sqrt[3]{ln(4-x^2)} is -(2x)/(3ln^{2/3)(4-x^2)(4-x^2)}

What is the first derivative of \sqrt[3]{ln(4-x^2)} ?

The first derivative of \sqrt[3]{ln(4-x^2)} is -(2x)/(3ln^{2/3)(4-x^2)(4-x^2)}

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derivative of

3 ln (4 - x^{2})

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

Solution steps

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

Apply the chain rule:

\frac{1}{3 ( ln ( 4 - x ^{2} ) ) ^{\frac{2}{3}}} \frac{d}{d x} (ln (4 - x^{2}))

= \frac{1}{3 ( ln ( 4 - x ^{2} ) ) ^{\frac{2}{3}}} \frac{d}{d x} (ln (4 - x^{2}))

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

= \frac{1}{3 ( ln ( 4 - x ^{2} ) ) ^{\frac{2}{3}}} (- \frac{2 x}{4 - x ^{2}})

Simplify

\frac{1}{3 ln ^{\frac{2}{3}} ( 4 - x ^{2} )} (- \frac{2 x}{4 - x ^{2}}) : - \frac{2 x}{3 ln ^{\frac{2}{3}} ( 4 - x ^{2} ) ( 4 - x ^{2} )}

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

y^{^{'}} = \frac{ln ( 2 )}{7} y - 20, y (0) = 200

\frac{w}{w + \frac{d}{w}}

\frac{d}{d x} (4 y - 2 x)

f (x) = 3 36 x^{2} + 10

\frac{\partial}{\partial x} (- 2 x - 8 y + 18)

What is the derivative of \sqrt[3]{ln(4-x^2)} ?
The derivative of \sqrt[3]{ln(4-x^2)} is -(2x)/(3ln^{2/3)(4-x^2)(4-x^2)}
What is the first derivative of \sqrt[3]{ln(4-x^2)} ?
The first derivative of \sqrt[3]{ln(4-x^2)} is -(2x)/(3ln^{2/3)(4-x^2)(4-x^2)}