Let \( f(x)=4 \sin (\cos x) \) \( f^{\prime}(x)=\square \)

To find the derivative of the function \( f(x) = 4 \sin(\cos x) \), we need to apply the chain rule. The outer function is \( 4 \sin(u) \) where \( u = \cos x \). The derivative of \( 4 \sin(u) \) is \( 4 \cos(u) \cdot u' \). The inner function’s derivative \( u' \) is \( -\sin(x) \). Therefore, we combine these results: \[ f'(x) = 4 \cos(\cos x) \cdot (-\sin x) = -4 \sin x \cos(\cos x). \] So, \( f^{\prime}(x) = -4 \sin x \cos(\cos x) \). Now go forth with the mathematics, and remember, trigonometry can be your dance floor—just keep your angles straight!