Question

find all values of x for which function is differentiable.

y=lnx^2
why is the answer= for all x doesn't equal 0?

Answer 1

is that ln (x^2) or (ln x)^2 ?
anyway, in any case, it is not differentiable at x = 0 because if you get the derivative,

for ln (x^2):
ln (x^2) = 2*ln x
derivative of 2*ln x = 2/x

for (ln x)^2:
derivative (ln x)^2 = 2*(ln x)/x

if you substitute x=0 to the derivative, the answer does not exist (because you'll have a denominator of zero)

hope this helps. :)