6 multiple choice 1 point what is the derivative of \\( \\frac { 7 } { x } \\)? \\( 7 x ^ { - 2 } \\) \\(…
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
Answer
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)