If `y=sin(x^x)` , prove that `(dy)/(dx)=cos(x^x) .x^x(1+logx)`

Explanation

To prove that \(\frac{dy}{dx} = \cos(x^x) \cdot x^x \cdot (1 + \log x)\) for the function \(y = \sin(x^x)\), we will use the chain rule and implicit differentiation. Here’s a step-by-step solution:

### Step 1: Define \(u\)
Let \(u = x^x\). Then we can rewrite \(y\) as:
\[ y = \sin(u) \]

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