Let `g(x)=(f(x))^3-3(f(x))^2+4f(x)+5x+3sinx+4cosxAAx in Rdot` Then prove that `g` is increasing whenever is increasing.

Explanation

To prove that the function \( g(x) = (f(x))^3 - 3(f(x))^2 + 4f(x) + 5x + 3\sin x + 4\cos x \) is increasing whenever \( f(x) \) is increasing, we need to analyze the derivative \( g'(x) \).

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

We start by differentiating \( g(x) \):

\[
g'(x) = \frac{d}{dx}\left((f(x))^3 - 3(f(x))^2 + 4f(x) + 5x + 3\sin x + 4\cos x\right)
...