What is the derivative of ln(sqrt(4-x^2)) ?

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

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

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

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derivative of

ln (4 - x^{2})

- \frac{x}{4 - x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{x}{4 - x ^{2}}

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