What is the derivative of arcsin(1-2x^2) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 - 2 x^{2}) = - 4 x

= \frac{1}{1 - ( 1 - 2 x ^{2} ) ^{2}} (- 4 x)

Simplify

\frac{1}{1 - ( 1 - 2 x ^{2} ) ^{2}} (- 4 x) : - \frac{2 2}{- 2 x ^{2} + 2}

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

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