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प्रश्न
Find the derivative of the following function from first principle.
(x – 1) (x – 2)
उत्तर
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
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