Question

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

Answer 1

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

Explanation:

We have the following expression:

`y=(10)/(3x^3)`

We rewrite and we would have:

`y=(10)/(3)\left((1)/(x^3)\right)`

Now we derive:

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

Finally, we simplify

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