Question

What is the derivative of the function g(x)=ln(cosx) ?

Answer 1

`d/dx ln(cosx) = -tanx`

Explanation:

Using the chain rule:

`d/dx ln(cosx) = 1/cosx d/dx (cosx) = -sinx/cosx = -tanx`

Answer 2

`-tanx`

Explanation:

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

`"given "y=f(g(x))" then"`

`dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"`

`d/dx(ln(cosx))`

`=1/cosx xxd/dx(cosx)=-sinx/cosx=-tanx`