Differentiate: ln(1+c) + ln(w-c)

Question

... The answer is 1/(1+c) - 1/(w-c) but I am confused on how the second term becomes negative ...

Answer 1

Dakota,

 

I'm doing to assume the variable here is c

 

As you know the derivative of ln(x) is 1/x, so

 

d/dc (ln(1+c) + ln(w-c)) = 1/(1+c) + 1/(w-c)(-1) = 1/(1+c) - 1/(w-c) 

 

This is because we have to use the chain rule to differentiate the (w-c) which is -1.

For the other terms we also differentiate (1+c) which is +1, which does not impact the answer.