`f(x) = x^2 - 5` Find the derivative of the function by the limit process.

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Chapter 2, 2.1 - Problem 18 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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  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. 

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