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

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

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

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

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

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

Solution steps

\frac{d}{d x} (arccos (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 arccos(1-2x^2) ?
The derivative of arccos(1-2x^2) is (2sqrt(2))/(sqrt(-2x^2+2))
What is the first derivative of arccos(1-2x^2) ?
The first derivative of arccos(1-2x^2) is (2sqrt(2))/(sqrt(-2x^2+2))