Question

For some constant $a$ and $b$, find the derivative of the following functions:
$(x-a)(x-b)$.

Answer 1

Let $f\left(x\right)=(x-a)(x-b)$
$\Rightarrow f\left(x\right)=x^2-(a+b)x+ab$
$\therefore f^{{}^{\prime }}\left(x\right)=\frac{d}{dx}(x^2-(a+b)x+ab)$
= $\frac{d}{dx}\left(x^2\right)-(a+b)\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(ab\right)$
$=2x-(a+b)+0=2x-a-b$