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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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