Derivative of y=2cosx-4√x

1. Differentiate $- 4 \sqrt{x} + 2 \cos{\left(x \right)}$ term by term:

   1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of cosine is negative sine:

         $$\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$$

      So, the result is: $- 2 \sin{\left(x \right)}$

   2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$

      So, the result is: $- \frac{2}{\sqrt{x}}$

   The result is: $- 2 \sin{\left(x \right)} - \frac{2}{\sqrt{x}}$

The answer is:

$$- 2 \sin{\left(x \right)} - \frac{2}{\sqrt{x}}$$