Question

If f(x) = ln(1 − 5x), then find f '(x).

Answer 1

The formula for the derivative of the ln function, with chain rule, is

(d/dx) ln u = (1/u)(du/dx).

Here, u = 1 - 5x, and du/dx = -5.

Then df/dx = [ 1 / 1-5x ]*(-5), or

df -5

---- = --------

dx 1-5x

Answer 2

`f(x)=\ln(1-5x)\\\\f'(x)=\left[\ln(1-5x)\right]'=(1)/(1-5x)\cdot(1-5x)'=(1)/(1-5x)\cdot(-5)=-(5)/(1-5x)\\\\Used:\\\\(\ln(x))'=(1)/(x)\\\\\left[g(f(x))]\right]'=g'(f(x))\cdot f'(x)`