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Using mathematical induction prove that ...

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

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To prove that \(\frac{d}{dx}(x^n) = n x^{n-1}\) for all positive integers \(n\) using mathematical induction, we will follow these steps: ### Step 1: Base Case We start by proving the base case where \(n = 1\). - **Left Hand Side (LHS)**: \[ \frac{d}{dx}(x^1) = \frac{d}{dx}(x) = 1 ...
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