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

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

What is:

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

?

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up vote 3 down vote accepted
  • Quotient rule on $\cfrac x{x+k}$
  • Product rule on $x(x+k)^{-1}$
  • Chain rule on $\left (1+\cfrac kx\right)^{-1}$
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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 $b(a+b)^-2$

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