Differentiate:

Question

Differentiate:

 

f(w) = w / (w +c/w)

Answer 1

Chris,

 

I recommend rewriting the original function to NOT have a complex fraction before taking the derivative with respect to "w".

 

Multiply top/bottom of the "big" fraction by w to get f(w) = w²/(w²+c)

 

Now use the quotient rule:

 

f'(w) = [(w²+c)2w - w²(2w)]/(w²+c)²

 

The numerator simplifies to 2cw.

 

Answer 2

We find the derivative of f in terms of w.  This means all the non-w terms are constants.

 

First, we rewrite the function so that it is easier to derive and reduce the number of steps to derive it.

 

f(w) = w / (w + cw^-1)

 

 

Now we use the quotient rule to derive.

 

f'(w) = [(1 + cw^-1) - w(1 - cw^-2)] / (w + cw^-1)²

 

 

Now just simplify.