Question

6 multiple choice 1 point what is the derivative of \\( \frac { 7 } { x } \\)? \\( 7 x ^ { - 2 } \\) \\( - 7 x ^ { - 2 } \\) \\( \ln ( 7 ) \\) \\( 7 x ^ { - 1 } \\) \\( 7 \ln ( x ) \\) \\( \ln ( 7 x ) \\) clear my selection

Explanation:

Step1: Rewrite the function

Rewrite \(\frac{7}{x}\) as \(7x^{-1}\) using the rule \(\frac{a}{x^n}=ax^{-n}\).

Step2: Apply the power rule

The power rule for differentiation is \(\frac{d}{dx}(ax^n)=anx^{n - 1}\). For \(y = 7x^{-1}\), where \(a = 7\) and \(n=-1\), we have \(\frac{d}{dx}(7x^{-1})=7\times(-1)x^{-1-1}\).

Step3: Simplify the expression

\(7\times(-1)x^{-1 - 1}=-7x^{-2}\)

Answer:

\(-7x^{-2}\) (the second option)