find the derivative of the function.\n$f(x)=8\\sqrt{x}+2\\cos(x)$\n$f(x)=$

Explanation:

Step1: Rewrite radical term

(8\sqrt{x} = 8x^{1/2})

Step2: Differentiate first term

(\frac{d}{dx}(8x^{1/2}) = 8 \cdot \frac{1}{2}x^{-1/2} = 4x^{-1/2} = \frac{4}{\sqrt{x}})

Step3: Differentiate second term

(\frac{d}{dx}(2\cos(x)) = 2(-\sin(x)) = -2\sin(x))

Step4: Sum derivatives

(f'(x) = \frac{4}{\sqrt{x}} - 2\sin(x))

Answer:

(\frac{4}{\sqrt{x}} - 2\sin(x))