if $f(x)=\frac{\tan x - 4}{sec x}$\n$f(x)=$\n$f(4)=$\nquestion help: video message instructor\nsubmit…

Explanation:

Step1: Simplify the function

We know that (\tan x=\frac{\sin x}{\cos x}) and (\sec x = \frac{1}{\cos x}). So (f(x)=\frac{\tan x - 4}{\sec x}=\sin x-4\cos x)

Step2: Differentiate the function

Using the derivative rules ((\sin x)'=\cos x) and ((\cos x)'=-\sin x). For (y = f(x)=\sin x-4\cos x), by the sum - rule of differentiation (y'=f'(x)=(\sin x)'-4(\cos x)') (f'(x)=\cos x + 4\sin x)

Step3: Evaluate the derivative at (x = 4)

Substitute (x = 4) into (f'(x)): (f'(4)=\cos(4)+4\sin(4))

Answer:

(f'(x)=\cos x + 4\sin x) (f'(4)=\cos(4)+4\sin(4))