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$\begingroup$

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

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

What is:

$\partial c \over \partial a$

?

2 Answers 2

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  • 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.2012-11-08
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$a/(a+b)= 1- b/(a+b)$ Thus the derivative is $b(a+b)^-2$