Find a formula for the derivative of the function g(x)=4x2−1

using difference quotients:
g′(x)=lim[(
h→0

1 answer

(g(x+h)-g(x))/h]

g′(x)= lim[(4(x+h)^2-1-4x^2+1)/h]

g′(x)= lim[(4x^2+8hx+4h^2-1-4x^2+1)/h]

g′(x)= lim[(8hx+4h^2)/h]

g′(x)= lim[8x+4h] as h→0

g′(x) = 8x