What is the derivative of ln(sqrt(3-x^2)) ?

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

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

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

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

- \frac{x}{3 - x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{x}{3 - x ^{2}}

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