How do you find f'(x) using the definition of a derivative for f(x)=x^2 - 1f(x)=x2−1?

1 Answer
Nico Ekkart
Oct 17, 2015

The derivative is 2x2x

Explanation:

Definition of a derivative:
\lim_(Deltax to 0) (f(x + Deltax) - f(x))/(Deltax)
Filling in your function:
\lim_(Deltax to 0) ((x + Deltax)^2-1 - x^2+1)/(Deltax)
= \lim_(Deltax to 0) (x^2 + 2xDeltax + Deltax^2 - x^2)/(Deltax)
= \lim_(Deltax to 0) (2xDeltax+Deltax^2)/(Deltax)
=\lim_(Deltax to 0) 2x+Deltax = 2x

Related questions
See all questions in Limit Definition of Derivative
Impact of this question
1647 views around the world
You can reuse this answer
Creative Commons License