What is the derivative of ln(1/(sqrt(1-x^2))) ?

The derivative of ln(1/(sqrt(1-x^2))) is x/(1-x^2)

What is the first derivative of ln(1/(sqrt(1-x^2))) ?

The first derivative of ln(1/(sqrt(1-x^2))) is x/(1-x^2)

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

\frac{x}{1 - x ^{2}}

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{x}{1 - x ^{2}}

What is the derivative of ln(1/(sqrt(1-x^2))) ?
The derivative of ln(1/(sqrt(1-x^2))) is x/(1-x^2)
What is the first derivative of ln(1/(sqrt(1-x^2))) ?
The first derivative of ln(1/(sqrt(1-x^2))) is x/(1-x^2)