From 4cb19ddd665575bb4b20265dfe406a1c124ae19f Mon Sep 17 00:00:00 2001 From: eggy Date: Wed, 28 Oct 2020 17:18:50 -0400 Subject: [PATCH] math: add higher order derivatives --- docs/mhf4u7.md | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/docs/mhf4u7.md b/docs/mhf4u7.md index 653e9fe..3952959 100644 --- a/docs/mhf4u7.md +++ b/docs/mhf4u7.md @@ -501,6 +501,15 @@ $$f´(x) = g´(h(x)) · h´(x)$$ $$f(x) = (4x^2-3x+1)^7$$ $$f´(x) = 7(4x^2-3x+1)^6 (8x-3)$$ +### Higher order derivatives + +The **second derivative** of $f(x)$ is the derivative of the first derivative of $f(x)$, that is, $f´´(x)$. + +The $n$th derivative of $f(x)$ is $f^{(n)}(x)$, and is the derivative of the $n-1$th derivative. It is written as $\frac{d^ny}{dx^n}$ in Leibniz notation. + +!!! example + The second derivative of an object's position with respect to time is its acceleration. See [SL Physics A#Displaying motion](/sph3u7/#displaying-motion) for more information. + ## Resources - [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)