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

To find the derivative of the function, we start with the equation:

$y = \frac{2}{\sqrt{x}} = 2x^{-\frac{1}{2}}$

We will use the power rule for differentiation, which states that if $y = ax^n$, then $\frac{dy}{dx} = n * ax^{n-1}$.

Applying the power rule:

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

This simplifies to:

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

Thus, the final answer is:

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