# How to differentiate amd simplify: ln(cosh(ln x) cos(x)) ?

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I like to set the problem equal to y if it is not already. Also it will help our case to rewrite the problem using properties of logarithms;

Now we do two substitutions to make the problem easier to read;

Let's say

and

now;

ahh, we can work with this :)

Let's take the derivative with respect to x of both sides. (Since none of our variables are x this will be implicit differentiation)

Well, we know the derivative of

So let's go back to

and

Plugging our newly found derivatives, and u, and w back into

If this can be simplified further, I haven't learned how. I hope this helped :)

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