What is the derivative of ln((arcsin(x)^2)) ?

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

What is the first derivative of ln((arcsin(x)^2)) ?

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

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\frac{d}{d x} (ln ((arcsin (x))^{2}))

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

Solution steps

\frac{d}{d x} (ln ((arcsin (x))^{2}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{140000}{x}

\int \frac{1}{x ^{2} - 3 x - 15} d x

\int 40 + 6 x - x^{2} d x

\int \frac{1}{x ( I n x ) ^{2}} d x

\frac{d}{d x} (tan (x) d x)

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