From 8cb32d54029fc06cea2812ce8b7f7bf723c1464b Mon Sep 17 00:00:00 2001 From: eggy Date: Sat, 31 Oct 2020 16:09:36 -0400 Subject: [PATCH] math: add implicit differentiation --- docs/mhf4u7.md | 15 +++++++++++++++ 1 file changed, 15 insertions(+) diff --git a/docs/mhf4u7.md b/docs/mhf4u7.md index a99eab5..43cc172 100644 --- a/docs/mhf4u7.md +++ b/docs/mhf4u7.md @@ -520,6 +520,21 @@ To identify the positive or negative regions of an equation, an interval line or 4. When crossing an x-intercept, if the degree of that factor is even, the sign stays the same; otherwise, it alternates. 5. Repeat for every other region. +### Implicit differentiation + +Implicit differentiation differentiates both sides of an equation with respect to $x$ and solves for $\frac{dy}{dx}$ ($y´$). Note that if $y$ is isolated, this is effectively the same as explicit differentiation. + +!!! warning + The **chain rule** must be applied when differentiating terms that contain $y$. + +!!! example + $$ + \frac{x^2}{4} + y^2 = 1 \\ + \frac{2x}{4} + 2y · \frac{dy}{dx} = 0 \\ + \frac{dy}{dx} = -\frac{\frac{x}{2}}{2y} \\ + \frac{dy}{dx} = -\frac{x}{4y} + $$ + ## Resources - [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)