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)

## Answer this Question

## Related Questions

Maths - differentiate from first principles y=1/x^2 i get to this then i get ...

math - differentiate from first principles 2x^3 -5 (f(x+h)-f(x))/h i know what ...

Calculus - Use the first principles definition to differentiate y = 5x^2. Please...

trigo help! - 1. differentiate cos(3/x) 2. differentiate sin(4/x) 3. ...

maths - differentiate using product, chain and quotient rule ln x / 5x-7 and e^x...

maths - prove that the following function is differentiable at x=0 using first ...

chemistry - Arrange the acids I) hydrogen selenate ion (HSeO− 4 ), pKa = 1...

maths - (a)(i)use the composite rule to differentiate the function f(x)=(x^2-6x+...

Chemistry; Please help - Write formulas for the following. 1. potassium ...

Statistics - Which of the following statements is not true about samples that ...