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Question

# Solve the given problems by finding the appropriate derivatives.Find the derivative of $y=\frac{x^2(1-2x)}{3x-7}$ in each of the following two ways. $(1)$ Do not multiply out the numerator before finding the derivative. $(2)$ Multiply out the numerator before finding the derivative. Compare the results.

Solution

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In this exercise, let's use the quotient rule to the expression to get the derivative of $y$. Let's assign

\begin{aligned} u=&x^2(1-2x)\\ v=&3x-7 \end{aligned}

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