Ok so I have a question, if f(x) is differentiable at all points how is log f(x) differentiable at all points because log f(x) is not differentiable for any negative x values.

Hey @Rehan_G,

Welcome, and we are glad that you could become a part of our community

I believe you are referring to the 8th question in the quiz. Note that in the question, it is specified that “Let f(x) be a positive real function”, i.e., `log(f(x))`

will always exist and will always be differentiable, as long as `f(x)`

is differentiable.

Now, let’s ignore the quiz once, and get back to this statement. First of all, `x`

can be negative as long as `f(x)`

is positive, because note that `f(x)`

is the input to the `log`

function, and not `x`

. Second, whenever we apply `log`

to any variable or function, we always impose the limit (*implicitly or explicitly*) that the input to `log`

must be greater than 0, since `log(x), for x <= 0`

doesn’t exist. So, the aspect of differentiability never arises here, since the function doesn’t even exist.

That’s why, in the quiz, it has been explicitly mentioned that `f(x)`

is a positive real function, i.e., `f(x) > 0`

. Let us know if this resolves your issue.

Cheers,

Elemento