Derivative question

1. Oct 9, 2007

codec9

I forgot how to take these derivatives. Could someone tell me the rule/work it out.

P = (doS1 + d1So) / (d1 + S1)

dP/dS1 = ?

I think it should be (denominator*d(numerator) - d(denom.)num.) / denom^2

but that gets the wrong answer.

2. Oct 9, 2007

HallsofIvy

Are do and d1 constants? In other words, is this the same as
$$P(x,y)= \frac{ax+ by}{b+ x}$$?
with z= do, b= d1, x= S1, y= So

In that case, yes, the partial derivative of P with respect to x is "(denominator*d(numerator) - d(denom.)num.) / denom^2"
(If So is also a constant, not a variable, then it is not a partial derivative but the same rule applies.)

3. Oct 9, 2007

codec9

OK, but the d(denominator) with respect to S1 which is a variable is 1, right?