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      <text>11.1.3a Key Point 2</text>
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      <text><![CDATA[Continuing with the example \(y(x)=x^2\), rather than looking at one point at a time we can consider a general point whose coordinates are \((x,x^2)\), the work above shows that the gradient (of the tangent) is given by \(2x\). <br><br>The function, \(2x\) which gives the gradient of \(y = x^2\) is called the <b>derivative</b> of \(y\) with respect to \(x\). It has other names too including the <b>rate of change</b> of \(y\) with respect to \(x\).
<p></p>
A special notation is used to represent the derivative. It is not a particularly user-friendly notation
but it is important to get used to it anyway. We write the derivative as \( \dfrac{dy}{dx} \), pronounced `dee \(y\) over dee \(x\)' or `dee \(y\) by dee \(x\)' or even `dee \(y\), dee \(x\)'.

\( \dfrac{dy}{dx} \) is not a fraction - so you can't do things like cancel the \(d\)'s - just remember that it is the symbol or notation for the derivative. An alternative notation for the derivative is \(y'\).


<div class="HELM_keypoint">
<h4>Key Point</h4>
<p>The derivative of \(y(x)\) is written  \( \dfrac{dy}{dx} \) or \( y'(x)\) or simply \(y'\)</p>
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