Given the function: $$y = \frac{1}{x^2}$$ Find an expression for \( \frac{dy}{dx} \) - AQA - A-Level Maths Pure - Question 1 - 2018 - Paper 1

To find ( \frac{dy}{dx} ), we will use the power rule of differentiation. The power rule states that if ( y = x^n ), then ( \frac{dy}{dx} = n \cdot x^{n-1} ).

In our case, we first rewrite the function as: $y = x^{-2}$

Now applying the power rule: $\frac{dy}{dx} = -2 \cdot x^{-3}$

We can simplify this to: $\frac{dy}{dx} = -\frac{2}{x^3}$

The expression for ( \frac{dy}{dx} ) is thus:

$\frac{dy}{dx} = -\frac{2}{x^3}$

However, since the question asks for an expression, we can also write it as:

$\frac{dy}{dx} = \frac{2}{x^3}$