Question

The derivative of the given function

Answer 1

Step-by-step explanation:

$y = { \sin}^{ - 1} (2x + 2) \\ \sin \: y = 2x + 2$

Differentating both sides wrt x,

$\frac{d}{dx} ( \sin \: y) = \frac{d}{dx} (2x + 2) \\ \cos \: y \times \frac{dy}{dx} = \frac{d}{dx} (2x) + \frac{d}{dx} (2) \\ \cos \: y \times \frac{dy}{dx} = 2 \frac{d}{dx} (x) + 0 \\ \cos \: y \times \frac{dy}{dx} = 2 \times 1 \\ \frac{dy}{dx} = \frac{2}{ \cos \: y } = \frac{2}{ \cos( { \sin}^{ - 1}(2x + 2) ) }$