but be aware: this assignment is set up to be auto - graded so you have immediate feedback.\nbe exactly the…

but be aware: this assignment is set up to be auto - graded so you have immediate feedback.\nbe exactly the same. on in - class assessments, you will be asked to write sentences and/or sl\nthese types of problems.\n1 multiple choice 1 point\nwhat is the derivative of $\\frac{6}{x^{3}}$?\n$6\\ln(x^{3})$\n$-18x^{-4}$\n$\\frac{1}{3x^{2}}$\n$6x^{-3}$\n$18x^{2}$\n$-18x^{-2}$\nclear my selection

but be aware: this assignment is set up to be auto - graded so you have immediate feedback.\nbe exactly the same. on in - class assessments, you will be asked to write sentences and/or sl\nthese types of problems.\n1 multiple choice 1 point\nwhat is the derivative of $\\frac{6}{x^{3}}$?\n$6\\ln(x^{3})$\n$-18x^{-4}$\n$\\frac{1}{3x^{2}}$\n$6x^{-3}$\n$18x^{2}$\n$-18x^{-2}$\nclear my selection

Answer

Explanation:

Step1: Rewrite the function

Rewrite (\frac{6}{x^{3}}) as (6x^{- 3}) using the rule (\frac{a}{x^{n}}=ax^{-n}).

Step2: Apply the power rule

The power rule for differentiation is (\frac{d}{dx}(x^{n})=nx^{n - 1}). For (y = 6x^{-3}), using the constant - multiple rule (\frac{d}{dx}(cf(x))=c\frac{d}{dx}(f(x))) (where (c = 6) and (f(x)=x^{-3})), we have (\frac{d}{dx}(6x^{-3})=6\frac{d}{dx}(x^{-3})). Then, by the power rule, (6\times(-3)x^{-3 - 1}).

Step3: Simplify the expression

(6\times(-3)x^{-3 - 1}=-18x^{-4})

Answer:

(-18x^{-4}) (the second option)