find all values of x for which function is differentiable.

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

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. :)

Well, it seems like you're not a fan of zeros, but don't worry, I won't clown around with the answer.

To determine the differentiability of the function y = ln(x^2), we should look out for any potential issues.

In this case, the function becomes problematic when x = 0. When x is exactly zero, the function is undefined, and the natural logarithm doesn't like undefined values.

However, for all other values of x, the function is smooth as silk and differentiable. So, we can say that the function y = ln(x^2) is differentiable for all x except when x equals 0.

So, in summary, the answer is that the function y = ln(x^2) is differentiable for all x except when x equals 0.

To determine the values of x for which the function y = ln(x^2) is differentiable, we need to consider the derivative of the function.

The derivative of y = ln(x^2) can be found using the chain rule:

dy/dx = (1/x^2) * 2x

Simplifying the expression, we have:

dy/dx = 2/x

For a function to be differentiable at a particular point, the derivative at that point should exist.

The derivative dy/dx = 2/x exists for all nonzero values of x. However, at x = 0, the derivative is undefined (since division by zero is not possible).

Therefore, the function y = ln(x^2) is differentiable for all values of x, except for x = 0.

To find the values of x for which the function y = ln(x^2) is differentiable, we need to consider the properties and conditions for differentiability of a function.

In this case, the function y = ln(x^2) is defined as the natural logarithm of the square of x. The natural logarithm function is differentiable for all positive values of x. However, it is important to note that the natural logarithm is not defined for values of x less than or equal to 0.

Therefore, in order for the function y = ln(x^2) to be differentiable, x must be a positive real number (x > 0). This means that the values of x for which the function is differentiable are all x-values that are greater than 0.

In other words, the answer is "for all x doesn't equal 0" because the function is not defined and therefore not differentiable at x = 0. For all other values of x greater than 0, the function is differentiable.