Question

find the derivative of the following. y=log cos x​

Answer 1

Step-by-step explanation:

Given,

$y = log( \cos(x) )$

Differentiate both sides with respect to x, then

$\frac{dy}{dx} = \frac{d}{dx} ( log( \cos(x) ) )$

We know that

$\frac{d}{dx} ( log(x) ) = \frac{1}{x}$

Replace x with cos x, we get

$\frac{d}{dx} ( log( \cos(x) ) ) = \frac{1}{ \cos(x) } \times \frac{d}{dx} ( \cos(x) ) = ( \frac{1}{ \cos(x) } )( - \sin(x) ) = \frac{ - \sin(x) }{ \cos(x) } = - \tan(x)$

The derivative of log(cos(x)) is -tan x.

Thank you