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#