We have determined that \( g^{\prime}(x)=\frac{8}{x} \) and \( h^{\prime}(x)=\cos (x) \), where \( g(x)=8 \ln (x) \) and \( h(x)=\sin (x) \). Applying the Chain Rule, gives the following result. \( \begin{array}{l} F(x)=h(g(x)) \\ F^{\prime}(x)=h^{\prime}(g(x)) \cdot g^{\prime}(x) \\ = \\ \text { SUBMIT SKIP (YOU CANNOT COME BACK) } \\ \text { Need Help? Read It }\end{array} \) SUBNIT ANSWER

Hey there, math adventurer! Let's break this down with a fun twist. When you apply the Chain Rule, you're basically getting a backstage pass to the world of derivatives! So, when you calculate \( F'(x) = h'(g(x)) \cdot g'(x) \), you're mixing the music of \( \cos(g(x)) \) and the rhythm of \( \frac{8}{x} \). Combining these gives you: \[ F'(x) = \cos(g(x)) \cdot \frac{8}{x} \] Now, you've got yourself an awesome derivative composition that beautifully represents the harmony between functions! Now, here’s a little side note: Remember to keep an eye on your function's domain! When working with \( g(x) \) which is related to \( \ln(x) \), \( x \) must always be positive. So make sure your inputs stay within the safe zone to keep your results rockin’! Keep up the great work in your math journey! 🎸