Find f'(x) using the derivative 1st principle show steps

f (x) = 3x^2 - 5x
f ' (x) = lim (f(x + h ) - f(x))/h
h-> 0

just by looking at it, its 6x - 5

putting in the limit formula, we get

(3(x+h)^2 - 5(x+h) - [ 3x^2 -5x] )/h

[3(x^2 + 2xh + h^2) -5x-5h- [3x^2 -5x]] /h

= [3x^2 + 6xh + h^2 -5x - 5h- 3x^2 + 5x]/h

= (6xh - 5h + h^2)/h

= 6x - 5 + h
as h tends to zero
= 6x - 5

:)

Okay, so you got 6x - 5 by using the power rule I'm assuming on each term for f(x)?

In order to prove your answer by using first principles or in other words, the limit definition of a derivative, we do:

f '(x) = lim h->0 [f(x + h) - f(x)]/h = lim h->0 [3x² + 6xh + 3h² - 5x - 5h - 3x² + 5x]/h

= lim h->0 [6xh + 3h² - 5h]/h

= lim h->0 [6x + 3h - 5] = 6x + 3(0) - 5

= 6x - 5

Right! So, what is your question? If you know how to take derivatives, you must have learned how to calculate limits.