How do you find the derivative of -5X by using limit process?

Answer 1

The derivative of f(x) is

lim h-->0 [f(x+h)-f(x)]/h.

So let f(x) = -5x. The derivative is

lim h-->0 [-5(x+h)- -5(x)]/h

= lim h-->0 [-5x - 5h + 5x]/h

= lim h-->0 -5h/h

Since the limit h-->0 of h/h is 1, the derivative is

-5