Describe all x values at which f is differentiable? f(x)=x^2-9

f(x)=I x^2-9 I   can be written as

f(x)  =  [ ( x^2 - 9)^2 ]^(1/2)

So....using the Chain Rule twice, we have :

f ' (x)  =  (1/2) [ (x^2 - 9)^2] ^(-1/2) [ 2 (x^2 - 9) *2x]  =

2x [ x^2 - 9] / [(x^2 - 9)^2] ^(1/2)   =

2x[x^2 - 9] /  l x^2 - 9 l

Note that if x = -3   or if x = 3, the derivative is undefined, because we can't divide by 0

Notice the "sharp points" at x = -3 and x = 3  on the graph :  https://www.desmos.com/calculator/ee9uapzsmi

The derivative is undefined at these points.......so.......this funnction is differentiable at all x except at x = -3  and x = 3