How do you use the limit definition of the derivative to find the derivative of f(x)=x^2?

1 Answer
Mar 1, 2017

f'(x)=2x

Explanation:

Given a function f(x) then by definition f'(x) = lim_"h->0" (f(x+h)-f(x))/h

In our example f(x) = x^2

:. f'(x) = lim_"h->0" ((x+h)^2-x^2)/h

= lim_"h->0" (x^2+2xh+h^2 - x^2)/h

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

= lim_"h->0" (2x+h )

=2x