Question

3 multiple choice 1 point what is the derivative of $-3x^{-3}$? $-9x^{-2}$ $9x^{-4}$ $-9x^{-4}$ $-9x^{-3}$ $9x^{-3}$ $9x^{-2}$ clear my selection

Explanation:

Step1: Apply the power rule

The power rule states that if \(y = ax^n\), then \(y^\prime=a\times n\times x^{n - 1}\). For \(y=-3x^{-3}\), \(a=-3\) and \(n = - 3\).

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Step2: Simplify the expression

Multiply \(-3\times(-3)=9\) and \(x^{-3 - 1}=x^{-4}\)

$$y^\prime = 9x^{-4}$$

Answer:

\(9x^{-4}\) (the second option)