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Popular >

derivative of ln(arcsin(x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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