Derivative Rules - Trigonometric Angle with Coefficient (with Rule) to Derivative

This math topic focuses on applying derivative rules to trigonometric functions that involve a coefficient with the angle variable. Specifically, the problems use the chain rule combined with basic trigonometric derivatives to find the derivatives of functions like cosine and sine, where the argument of the trigonometric function is a linear expression of \(x\). Each function is presented in the form \(f(x) = a \cdot \text{trig function}(b \cdot x)\), and students are tasked with deriving these to practice fluency in chain rule applications and differentiation of trigonometric functions.