If f(x)=4sinx/3+cosx, then
f'(x)f′(x) =   

f'(3)f′(3) = 


Given that the function is \( f(x) = \frac{4\sin(x)}{3} + \cos(x) \), we will first compute its derivative \( f'(x) \) using standard differentiation rules.

### Step 1: Differentiate \( f(x) \)

The function consists of two terms: \( \frac{4\sin(x)}{3} \) and \( \cos(x) \).

1. The derivative of \( \frac{4\sin(x)}{3} \) is:
   \[
   \frac{4}{3} \cdot \frac{d}{dx}[\sin(x)] = \frac{4}{3} \cos(x)
   \]
   
2. The derivative of \( \cos(x) \) is:
   \[
   \frac{d}{dx}[\cos(x)] = -\sin(x)
   \]

Thus, the derivative of \( f(x) \) is:
\[
f'(x) = \frac{

If f(x) = 4sin(x)/3 + cos(x), then f'(x) = ? and f'(3) = ?

Learn how to differentiate the trigonometric function f(x) = 4sin(x)/3 + cos(x) and find f'(x) and f'(3). This solution uses standard differentiation rules and trigonometric derivatives, suitable for students in Grades 11-12.

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