Question

Using the Constant Multiple Rule, complete the table to find the derivative of the function without using the Quotient Rule.

Answer 1

ANSWER:

$\begin{gathered} \text{ Rewrite} \\ \\ y=\frac{10}{3}\frac{1}{x^{3}} \\ \\ \text{ Differentiate} \\ \\ y^{\prime}=\frac{10}{3}(-3x^{-4}) \\ \\ \text{ Simplify} \\ \\ y^{\prime}=-\frac{10}{x^{4}} \end{gathered}$

STEP-BY-STEP EXPLANATION:

We have the following expression:

$y=\frac{10}{3x^3}$

We rewrite and we would have:

$y=\frac{10}{3}\left(\frac{1}{x^3}\right)$

Now we derive:

$\begin{gathered} y^{\prime}=\frac{10}{3}\frac{d}{dx}\left(\frac{1}{x^3}\right) \\ \\ y^{\prime}=\frac{10}{3}\left(-3x^{-3-1}\right) \\ \\ y^{\prime}=\frac{10}{3}(-3x^{-4}) \end{gathered}$

Finally, we simplify

$\begin{gathered} y^{\prime}=\frac{10}{3}(-3x^{-4})=-10x^{-4} \\ \\ y^{\prime}=-\frac{10}{x^4} \end{gathered}$