Problem
(1) What is the derivative of the function $f(x)=\frac{1}{x^{6}}$ (A) $\frac{6}{x^{7}}$ (B) $6 x^{5}$ (c) $\frac{-6}{x^{5}}$ (D) $\frac{-6}{x^{7}}$
Solution
Step 1 ：Rewrite the function as $f(x)=x^{-6}$
Step 2 ：Apply the power rule for differentiation: $f'(x)=-6x^{-7}$
Step 3 ：\( \boxed{\frac{-6}{x^{7}}} \)
