Calculus of a Single Variable, Chapter 2, 2.1, Section 2.1, Problem 18

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.