Find `dy/dx` if `2^(x)+2^(y)=2^(x+y)`

Explanation

To find \( \frac{dy}{dx} \) given the equation \( 2^x + 2^y = 2^{x+y} \), we will use implicit differentiation. Here’s a step-by-step solution:

### Step 1: Differentiate both sides with respect to \( x \)
We start with the equation:
\[ 2^x + 2^y = 2^{x+y} \]
Differentiating both sides with respect to \( x \):
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