Derivatives of Trig Functions

Question

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

Options:

1. 
2. (1 - x)²
3. 
4. 

Answer 1

The derivative of ln(u) is (1/u)*du

where u can be just a constant or some function containing a variable such as x

we multiply by the derivative of u if it is a function of another variable such as x because of the chain rule

so the derivative of ln(1-x) is 1/(1-x) times the derivative of 1-x which is -1

so the answer is -1*(1/1-x) which can be simplified to

1/x-1 or answer 4