Differentiate each of the following. a. y = (3x² - x)³
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We will use the chain rule. Let $u = 3x^2 - x$. Then $y = u^3$. We have $\frac{dy}{du} = 3u^2$ and $\frac{du}{dx} = 6x - 1$. By the chain rule, $\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} = 3u^2 (6x - 1)$. Substituting $u = 3x^2 - x$, we have Show more…
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