How do I differentiate an expression of the form y = (ax+b)^n?
In order to differentiate this we need to use the chain rule- first let u = ax + b. Then differentiating, du/dx = a. By substituting into the original expression, we can obtain y = u^n. Differentiating that gives dy/du = nu^(n-1). Since, using the chain rule, dy/dx = du/dx * dy/du = anu^(n-1). Subbing back in for u, we obtain our answer: an(ax+b)^(n-1).
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