Differentiate.
\[
\begin{array}{l}
f(x)=4 \sin (x)-3 \cos (x) \\
f^{\prime}(x)=\square
\end{array}
\]

Answer

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Answer

So, the derivative of the function \(f(x) = 4\sin(x) - 3\cos(x)\) is \(\boxed{f'(x) = 4\cos(x) + 3\sin(x)}\)

Steps

Step 1 ：Given the function \(f(x) = 4\sin(x) - 3\cos(x)\)

Step 2 ：Apply the rules of differentiation, where the derivative of \(\sin(x)\) is \(\cos(x)\) and the derivative of \(\cos(x)\) is \(-\sin(x)\)

Step 3 ：So, the derivative of the function is \(f'(x) = 4\cos(x) - (-3\sin(x))\)

Step 4 ：Simplify to get \(f'(x) = 4\cos(x) + 3\sin(x)\)

Step 5 ：So, the derivative of the function \(f(x) = 4\sin(x) - 3\cos(x)\) is \(\boxed{f'(x) = 4\cos(x) + 3\sin(x)}\)