Question

Differentiate tan √cos x using the chain rule.

Answer 1

Step-by-step explanation:

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