Posted by **chrystabelle** on Friday, January 20, 2012 at 3:22am.

DIFFERENTIATE FROM FIRST PRINCIPLES

(I)3X

(ii)X^2+2X+3

(iii)1/x^2

- maths -
**Reiny**, Friday, January 20, 2012 at 10:06am
I will do the middle one, you do others, looks like an assignment.

f(x) = x^2 - 2x + 3

dy/dx = LIM [ f(x+h) - f(x) ]/h as h---> 0

f(x+h) = (x+h)^2 + 2(x+h) + 3

= x^2 + 2xh + h^2 + 2x + 2h + 3

Lim [ f(x+h) - f(x) ]/h

= lim (x^2 + 2xh + h^2 + 2x + 2h + 3 - (x^2 + 2x + 3)/h

= lim (2xh + h^2 + 2h)/h

= lim 2x + h + 2

= 2x + 2

(each of the "lim" has h--> 2 under it)

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