What is the derivative of ln(arccos(x)) ?

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

What is the first derivative of ln(arccos(x)) ?

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

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\frac{d}{d x} (ln (arccos (x)))

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

Solution steps

\frac{d}{d x} (ln (arccos (x)))

Apply the chain rule:

\frac{1}{arccos ( x )} \frac{d}{d x} (arccos (x))

= \frac{1}{arccos ( x )} \frac{d}{d x} (arccos (x))

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

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

Simplify

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

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

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