let ( f(x)=3sin(x)+11cos(x) ). find the following:\n1. ( f(x)=)\n2. ( f(3)=)

Explanation:

Step1: Differentiate (f(x))

Use the derivative rules: ((\sin x)'=\cos x) and ((\cos x)'=-\sin x). For (f(x) = 3\sin(x)+11\cos(x)), by the sum - rule ((u + v)'=u'+v') where (u = 3\sin(x)) and (v = 11\cos(x)). The derivative of (u): ((3\sin(x))'=3\cos(x)) (using the constant - multiple rule ((cf(x))'=cf'(x)) with (c = 3) and ((\sin x)'=\cos x)). The derivative of (v): ((11\cos(x))'=- 11\sin(x)) (using the constant - multiple rule ((cf(x))'=cf'(x)) with (c = 11) and ((\cos x)'=-\sin x)). So, (f'(x)=3\cos(x)-11\sin(x)).

Step2: Evaluate (f'(3))

Substitute (x = 3) into (f'(x)). (f'(3)=3\cos(3)-11\sin(3)).

Answer:

1. (f'(x)=3\cos(x)-11\sin(x))
2. (f'(3)=3\cos(3)-11\sin(3))