Can you find the difference quotient with steps

Question

use the function f(x)= x^2-16 and using formula f(x+h)-f(x)/h

Answer 1

[(x+h)^2 -16 - x^2 +16]/h = (x^2 +2xh + h^2 - 16 -x^2 +16)/h = (2xh+h^2)/h = 2x+h

as h approaches zero the difference quotient approaches 2x

f(x) = x^2 -16

f'(x) = 2x = the derivative of f(x)

shortcut rule for finding derivative of a term is make the exponent the coefficient and reduce the exponent by 1. derivative of x^2 = 2x^(2-1) = 2x. derivative of a constant term = 0