10. Demonstrate and explain how to find the derivative of the following functions. Be sure to explicitly denote which derivative rules (scalar multiple, sum/difference, quotient, etc.) you are using in your work. \( \begin{array}{l}\text { (h) } \\ h(y)=2 \cos (y)-e^{y}\end{array} \)

To find the derivative of the function \( h(y) = 2 \cos(y) - e^y \), we can apply the sum/difference rule and the scalar multiple rule. According to the sum/difference rule, the derivative of a sum or difference of functions is the sum or difference of their derivatives. 1. First, differentiate \( 2 \cos(y) \): using the scalar multiple rule, we take the derivative of \( \cos(y) \), which is \(-\sin(y)\), and multiply by 2. Thus, \( \frac{d}{dy}(2 \cos(y)) = 2 \cdot (-\sin(y)) = -2\sin(y) \). 2. Second, differentiate \( -e^y \): since the derivative of \( e^y \) is itself, we have \( \frac{d}{dy}(-e^y) = -e^y \). Combining these results gives us \( h'(y) = -2\sin(y) - e^y \). So, the final answer is \( h'(y) = -2\sin(y) - e^y \).