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

2 Answers
Jun 24, 2018

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

Explanation:

Using the chain rule:

d/dx ln(cosx) = 1/cosx d/dx (cosx) = -sinx/cosx = -tanxddxln(cosx)=1cosxddx(cosx)=sinxcosx=tanx

Jun 24, 2018

-tanxtanx

Explanation:

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

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