Prove dy/dx = nx^(n-1), if y = x^n and n = positive integers

Prove dy/dx = nx^(n-1), if y = x^n and n = positive integers. To prove this, we will equate delta y equals to [(x + delta x)^n] - y. Applying the binomial theorem to (x + delta x)^n, simplify it. Divide both sides of the equation by delta x to simplify the right-hand side members of the equation. Simplify it.

After the necessary simplification, we will use the formula dy/dx = the limit of [(delta y)/(delta x)] as delta x approaches to zero. Apply the said limit to [(delta y)/(delta x)] as delta x approaches to zero. After applying the said limit, the term nx^(n-1) remains. And by that, we've proven dy/dx = nx^(n-1).

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