For some constants a and b, find the derivative of (x − a) (x − b)

Let f (x) = (x – a) (x – b)

\( f(x)=x^2-(a+b)+ab\)

\( f'(x)=\dfrac{d}{dx}(x^2-(a+b)x+ab)\)

\( \dfrac{d}{dx}(x)^2-(a+b)\dfrac{d}{dx}(x)+\dfrac{d}{dx}(ab)\)

On using theorem \( \dfrac{d}{dx}(x^n)=nx^{n-1}\), we obtain

\( f'(x)=2x-(a+b)+0\)

=2x-a-b