# How do you find the derivative of #y=ln(cos(x))# ?

##### 2 Answers

You can find this derivative by applying the Chain Rule, with

**Process:**

To apply the chain rule, we first find the derivative of the outer function,

Now we just need to find the derivative of the inner function,

Since the derivative of

#dy/dx = (1/cosx) * (-sinx) = (-sinx/cosx) = -tanx# .

A shorter way to do these is to just know that the derivative of a

#### Explanation:

#"differentiate using the "color(blue)"chain rule"#

#• d/dx(ln(f(x)))=(f'(x))/(f(x))#

#rArrdy/dx=(-sinx)/(cosx)=-tanx#