What is the derivative of 1/(arcsin(x)) ?

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

What is the first derivative of 1/(arcsin(x)) ?

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

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{x}{( x + y )})

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

\int 2 x (x^{2} + 1)^{8} d x

(g (x))^{3}

x \to 0 lim (x^{3} e^{- x^{2}})

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