Question

Differentiate y = arccos(1-2x²) with respect to x, and simplify your answer.

Answer 1

use the chain rule\[\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}\]\[y = \arccos \left(1 - 2x^2\right)\]\[u = 1 - 2x^2\]\[\frac{dy}{dx} = \frac{d}{du}\left( \arccos u \right) \frac{d}{dx}\left( 1 - 2x^2 \right)\]try to differentiate it by yourself, after that you need to simplify the answer

Answer 2

\[\frac{dy}{dx} = \frac{d(arccosu)}{du} \frac{d(1 - 2x^2)}{dx}\]\[\frac{dy}{dx}=\frac1{\sqrt{1-u^2}}\times(-4x)\]Is this correct?

Answer 3

almost, remember\[\frac{d}{dx}\left( \arccos x \right) = - \frac{1}{\sqrt{1 - x^2}}\]after you differentiate it, substitute u = 1 - 2x^2 back and simplify