If `y=e^xcosx` , prove that `(dy)/(dx)=sqrt(2)\ e^xcos(x+pi/4)`

Explanation

To prove that \(\frac{dy}{dx} = \sqrt{2} e^x \cos(x + \frac{\pi}{4})\) for the function \(y = e^x \cos x\), we will use the product rule of differentiation.

### Step-by-Step Solution:

1. **Identify the function**:
\[ y = e^x \cos x \]
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