What is the derivative of arcsin(-x) ?

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

What is the first derivative of arcsin(-x) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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