Question

Find the derivative of the following function from first principal (1) (x -1) ( x -2 )​

Answer 1

Answer:

Step-by-step explanation:

We have,

$f(x) = (x - 1)(x - 2)={x}^{2} - 3x +2$

$f^{'}(x) = \lim_{h \rarr 0}\frac{f(x + h) - f(x)}{h}$

$f^{'}(x) = \lim_{h \rarr 0}\frac{(x + h)^{2}-3(x + h)+2 -{x}^{2} + 3x -2 }{h}$

$f^{'}(x) = \lim_{h \rarr 0}\frac{x^{2} + h^{2} +2xh -3x - 3h+2 -{x}^{2} + 3x -2 }{h}$

$f^{'}(x) = \lim_{h \rarr 0}\frac{ h^{2} +2xh - 3h }{h}$

$f^{'}(x) = \lim_{h \rarr 0}(h +2x - 3)$

$f^{'}(x) =( 2x - 3)$