Prove that `(x/a)^n+(y/b)^n=2` touches the straight line `x/a+y/b=2` for all `n in N` , at the point `(a ,\ b)` .

Explanation

To prove that the curve \((\frac{x}{a})^n + (\frac{y}{b})^n = 2\) touches the straight line \(\frac{x}{a} + \frac{y}{b} = 2\) at the point \((a, b)\) for all \(n \in \mathbb{N}\), we will follow these steps:

### Step 1: Differentiate the Curve
We start with the equation of the curve:
\[ \left(\frac{x}{a}\right)^n + \left(\frac{y}{b}\right)^n = 2 \]
We will differentiate both sides with respect to \(x\).
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