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components/sections/derivatives/content.en-GB.md
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# Derivatives
There's a number of useful things that you can do with Bézier curves based on their derivative, and one of the more amusing observations about Bézier curves is that their derivatives are, in fact, also Bézier curves. In fact, the derivation of a Bézier curve is relatively straight forward, although we do need a bit of math. First, let's look at the derivative rule for Bézier curves, which is:
There's a number of useful things that you can do with Bézier curves based on their derivative, and one of the more amusing observations about Bézier curves is that their derivatives are, in fact, also Bézier curves. In fact, the differentiation of a Bézier curve is relatively straight forward, although we do need a bit of math. First, let's look at the derivative rule for Bézier curves, which is:
\[
Bézier'(n,t) = n \cdot \sum_{i=0}^{n-1} (b_{i+1}-b_i) \cdot Bézier(n-1,t)_i