Find the derivative of the following:
$\displaystyle y = (2x - 5)(4 - x)^{-1}$
I got $\displaystyle y' = 2x(4 - x)^{-1} + (2x - 5)(4 - x)^{-2}$ or $\displaystyle y' = \frac{2x}{4 - x} + \frac{2x - 5}{(4 - x)^2}$
Correct?
$\displaystyle y' = 2x(4 - x)^{-1} + (2x - 5)(4 - x)^{-2}$ or $\displaystyle y' = \frac{2x}{4 - x} + \frac{2x - 5}{(4 - x)^2}$ looks wrong to me.
You've got your product rule okay, but when you differentiated $\displaystyle 2x-5$ you got $\displaystyle 2x$ rather than $\displaystyle 2$.
A simple slip-up, it's so easy to do - other than that the technique is fine.