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

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

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

Answer

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). [ \begin{align*} y^\prime&=-3\times(-3)\times x^{-3-1}\ \end{align*} ]

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)