Question

What is the derivative of `ln(cos2x)`?

Answer 1

`-2tan2x`

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"`

`rArrd/dx(ln(cos2x))`

`=1/(cos2x)xxd/dx(cos2x)`

`=1/(cos2x)xx-sin2x xxd/dx(2x)`

`=-2xx(sin2x)/(cos2x)=-2tan2x`