Question

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

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:

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