What is the derivative of ln(sqrt(4-3x^3)) ?

The derivative of ln(sqrt(4-3x^3)) is -(9x^2)/(2(4-3x^3))

What is the first derivative of ln(sqrt(4-3x^3)) ?

The first derivative of ln(sqrt(4-3x^3)) is -(9x^2)/(2(4-3x^3))

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

- \frac{9 x ^{2}}{2 ( 4 - 3 x ^{3} )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 - 3 x^{3}) = - \frac{9 x ^{2}}{2 4 - 3 x ^{3}}

= \frac{1}{4 - 3 x ^{3}} (- \frac{9 x ^{2}}{2 4 - 3 x ^{3}})

Simplify

\frac{1}{4 - 3 x ^{3}} (- \frac{9 x ^{2}}{2 4 - 3 x ^{3}}) : - \frac{9 x ^{2}}{2 ( 4 - 3 x ^{3} )}

= - \frac{9 x ^{2}}{2 ( 4 - 3 x ^{3} )}

What is the derivative of ln(sqrt(4-3x^3)) ?
The derivative of ln(sqrt(4-3x^3)) is -(9x^2)/(2(4-3x^3))
What is the first derivative of ln(sqrt(4-3x^3)) ?
The first derivative of ln(sqrt(4-3x^3)) is -(9x^2)/(2(4-3x^3))