I'm having trouble figuring out how to find the partial derivative of Q with respect to b and d.
The book I'm using shows me the answer, but not the steps. The function is:
Q = (d - b) / (a + c)
here is how I think it would be done:
The partial derivative of Q with respect to b is: (d - b) / (a + c) = (d - b)(a + c)^-1 then drop d as it is a constant and put -b to -1 as it is the variable. -b/(a + c) but the book shows that it should be 1/(a+b)
For the partial differential of Q with respect to d I do get the right answer (d - b) / (a + c) = 1/(a + c) though, but I'm not sue if that is just luck, rather than using the right method.
Thanks for the help!
You are looking at the function $$Q=\frac{d-b}{a+c}$$ As long as you do not need the derivative of $Q$ with respect to $a$ or $c$, the denominator is a constant. So, $$Q'_b=\frac{1}{a+c} (d-b)'_b=\frac{-1}{a+c}$$ Similarly, $$Q'_d=\frac{1}{a+c} (d-b)'_d=\frac{1}{a+c}$$ So, there must be a typo in your book and you are right !
If you need to consider the other derivatives which involve a quotient, jus post and I shall continue.