Question

Find the derivative of the following function from first principle.

(x – 1) (x – 2)

Answer 1

Let f(x) = (x – 1) (x – 2) Accordingly, from the first principle,

`f'(x) = lim_(h->0) (f(x + h) - f(x))/h`

= `lim_(h->0)((x + h - 1) (x + h - 2) -(x - 1) (x - 2))/h`

= `lim_(h->0)((x^2 + hx -2x + hx + h^2 - 2h - x - h + 2) - (x^2 - 2x - x + 2))/h`

= `lim_(h->0)((hx + hx + h^2 - 2h - h))/h`

= `lim_(h->0) (2hx + h^2 - 3h)/h`

= `lim_(h->0) (2x + h - 3)`

= (2x + 0 - 3)

= 2x - 3