I am trying to differentiate this equation.
I have done it one way and got this solution (I don't know how to put it into Math formatting):
$b-2x-xy/(1+x)^2$
I used the quotient rule, and took out $y$ as a constant.
However when I looked at the solutions, my lecturer got:
$b-2x-y/(1+x)+(xy)/(1+x)^2$
I've simplified her solution so I know mine is right. However in order to complete the rest of the question it's far easier to have it in her form.
Can someone please walk me through, step by step, how to get this solution? I'm getting myself very confused.
Thanks in advance.
Original Question: I am working on part a.3. I have to find the Jacobian, and set the trace equal to zero and to start I need to find the derivative of x(dot) with respect to x.
You've multiplied $x$ with each of the terms in the parenthesis, and you took the derivative. You got the first two terms right. The last one is $$-\frac{xy}{1+x}$$You can use product rule, where the first function is $x$ and the second is $-y/(1+x)$. So the derivative of that is $$-\frac y{1+x}-x\frac{-y}{(1+x)^2}$$
If you use the quotient rule, you don't have a constant $y$ at the numerator, but you have $xy$ instead.