Using mathematical induction prove that : `d/(dx)(x^n)=n x^(n-1)` for all `n in N`.

Explanation

To prove that \(\frac{d}{dx}(x^n) = n x^{n-1}\) for all \(n \in \mathbb{N}\) using mathematical induction, we will follow these steps:

### Step 1: Base Case
We first check the base case for \(n = 1\).

- **Left-hand side (LHS)**: \(\frac{d}{dx}(x^1) = \frac{d}{dx}(x) = 1\)
- **Right-hand side (RHS)**: \(1 \cdot x^{1-1} = 1 \cdot x^0 = 1\)

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