You need to evaluate derivative of the function f'(x) such that:

`f'(x) = lim_(h-gt0) (sqrt(5x + 5h + 3) - sqrt(5x+3))/h`

You need to multiply fraction by conjugate of `(sqrt(5x + 5h + 3) - sqrt(5x+3))` such that:

`f'(x) = lim_(h-gt0) ((sqrt(5x + 5h + 3) - sqrt(5x+3))(sqrt(5x + 5h + 3)+ sqrt(5x+3)))/(h((sqrt(5x + 5h + 3)+ sqrt(5x+3)) ))`

You need to use the special product `a^2 - b^2 = (a-b)(a+b)`

`((sqrt(5x + 5h + 3) - sqrt(5x+3))(sqrt(5x + 5h + 3) + sqrt(5x+3))) = 5x + 5h + 3 - 5x - 3`

Reducing like terms yields:

`((sqrt(5x + 5h + 3) - sqrt(5x+3))(sqrt(5x + 5h + 3) + sqrt(5x+3))) = 5h`

`f'(x)= lim_(h-gt0) (5h)/(h(sqrt(5x + 5h + 3) + sqrt(5x+3))) `

`f'(x)= lim_(h-gt0) 5/(sqrt(5x + 5h + 3) + sqrt(5x+3))`

`f'(x)= 5/(2sqrt(5x+3))`

**Hence, evaluating the first derivative of function using first principle yields `f'(x)= 5/(2sqrt(5x+3)).` **

**Further Reading**

## 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