The given mathematical problem requires the determination of the first derivative of a function and its evaluation at a specific point.**Problem Statement:**Given the function: \( f(x) = 2 \sin x + 9 \cos x \), find the following:1. The first derivative of the function, denoted as \( f'(x) \).2. The value of the first derivative at \( x = 4 \), denoted as \( f'(4) \).**Solution Steps:**1. **Finding \( f'(x) \)**: - The first derivative of the function \( f(x) \) with respect to \( x \) is obtained by differentiating each term of the function. - The derivative of \( 2 \sin x \) is \( 2 \cos x \). - The derivative of \( 9 \cos x \) is \( -9 \sin x \). - Therefore, \( f'(x) = 2 \cos x - 9 \sin x \).2. **Evaluating \( f'(4) \)**: - Substitute \( x = 4 \) into the first derivative: - \( f'(4) = 2 \cos 4 - 9 \sin 4 \).In conclusion:- \( f'(x) = \boxed{2 \cos x - 9 \sin x} \)- \( f'(4) = \boxed{2 \cos 4 - 9 \sin 4} \)This problem illustrates the application of differentiation on trigonometric functions and the evaluation of the derived function at a given point.

Name: The given mathematical problem requires the determination of the firs
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: The given mathematical problem requires the determination of the first derivative of a function and its evaluation at a specific point.**Problem Statement:**Given the function: \( f(x) = 2 \sin x + 9 \cos x \), find the following:1. The first deriva