Question

let ( h(x)=\frac{1}{x^{6}} ). ( h^{prime}(1)= )

Explanation:

Step1: Rewrite the function

Rewrite \( h(x)=\frac{1}{x^{6}} \) as \( h(x)=x^{-6} \).

Step2: Apply the power rule

The power rule is \( (x^{n})^\prime = nx^{n - 1} \). For \( h(x)=x^{-6} \), \( h^\prime(x)=-6x^{-6 - 1}=-6x^{-7}=-\frac{6}{x^{7}} \).

Step3: Substitute \( x = 1 \)

Substitute \( x = 1 \) into \( h^\prime(x) \). \( h^\prime(1)=-\frac{6}{1^{7}}=-6 \).

Answer:

\(-6\)