To find the derivative of the function `f(x)=x^2-5`

` `

using the limit process, use the formula

`m=lim_(h->0)(f(x+h)-f(x))/h`

` `

`m=lim_(h->0)(((x+h)^2-5)-(x^2-5))/(h)`

`m=lim_(h->0)((x^2+2xh+h^2-5)-x^2+5)/(h)`

`m=lim_(h->0)(2xh+h^2)/h`

`m=lim_(h->0)(h(2x+h))/h`

`m=lim_(h->0)(2x+h)`

When you substitute the 0 in for h, the slope m is 2x. Therefore the derivative of the function `f(x)=x^2-5`

is `f'(x)=2x`

**The answer is 2x.**

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now