A curve has equation $y = \frac{2}{\sqrt{x}}$ Find $rac{dy}{dx}$ Circle your answer. - AQA - A-Level Maths Mechanics - Question 2 - 2017 - Paper 1

To find the derivative rac{dy}{dx} of the function $y = \frac{2}{\sqrt{x}}$, we can rewrite it in a simpler form:

$y = 2x^{-1/2}$

Now we apply the power rule for differentiation, which states that if $y = x^n$, then rac{dy}{dx} = nx^{n-1}.

Thus, we get:

$\frac{dy}{dx} = 2 \cdot \left(-\frac{1}{2}\right)x^{-3/2} = -\frac{1}{\sqrt{x} \cdot x} = -\frac{1}{x\sqrt{x}}$

This simplifies to:

$\frac{dy}{dx} = -\frac{1}{x\sqrt{x}}$

Therefore, the answer is

$-\frac{1}{x\sqrt{x}}$.