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}

\int \frac{r ^{2} - 1 0 ^{r} + 4}{r ^{3}} d r

\int_{3}^{\infty} \frac{1}{x ^{2} + x} d x

\frac{d}{d x} ((3 x - 2)^{4})

x^{7} sin (x)

\int 2 x (x^{2} + 6)^{9} d 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))