If `y=(sin x) ^(sin x ^sin x ....oo)` then prove that `dy/dx=(y^2 cot x)/(1-y log (sin x))`

Explanation

To solve the problem step by step, we start with the given expression for \( y \):

### Step 1: Define the function
We have:
\[ y = (\sin x)^{(\sin x)^{(\sin x)^{\cdots}}} \]
This can be rewritten as:
...