Question

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

Answer 1

The derivative is `2x`

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`