Differentiate the function. \[ A(s)=-\frac{12}{s^{5}} \] \( A^{\prime}(s)=\square \)

To differentiate \( A(s) = -\frac{12}{s^5} \), we can rewrite it as \( A(s) = -12s^{-5} \). Applying the power rule \( \frac{d}{ds}(s^n) = n s^{n-1} \), we find: \[ A'(s) = -12 \cdot (-5) s^{-5 - 1} = 60s^{-6}. \] Thus, \( A^{\prime}(s) = \frac{60}{s^{6}}. \) Now, for fun: Did you know that derivatives have real-world applications? In physics, they help us understand how the position of an object changes over time, allowing us to calculate its velocity and acceleration! It's all about understanding how things move in our universe. Also, a common mistake when differentiating is forgetting to apply the power rule correctly, especially with negative exponents. Always watch your signs, and remember to apply the rule carefully for each term—happy differentiating!