# Derivative of $x \over x+k$?

This seems like it should be easy but its got me beat:

$$c = {a \over {a + b} }$$

What is:

$$\partial c \over \partial a$$

?

-

• Quotient rule on $\cfrac x{x+k}$
• Product rule on $x(x+k)^{-1}$
• Chain rule on $\left (1+\cfrac kx\right)^{-1}$
For some embarassing reason I can't explain I thought that because the numerator and denominator shares the $a$ term the Quotient Rule didn't apply. Sorry. –  Andrew Tomazos Nov 8 '12 at 13:33
$a/(a+b)= 1- b/(a+b)$ Thus the derivative is $b(a+b)^-2$