From 4c492006f24c2d8629f148886b9a83db70dec3e2 Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Wed, 27 Mar 2019 09:44:24 +1100 Subject: [PATCH 1/1] [spec] rates --- spec/calculus.md | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/spec/calculus.md b/spec/calculus.md index ee88068..c59c4b7 100644 --- a/spec/calculus.md +++ b/spec/calculus.md @@ -245,3 +245,15 @@ $\int k f(x) dx = k \int f(x) dx$ To find stationary points of a function, substitute $x$ value of given point into derivative. Solve for ${dy \over dx}=0$. Integrate to find original function. +## Rates + +### Related rates + +$${da \over db} \quad \text{change in } a \text{ with respect to } b$$ + +#### Gradient at a point on parametric curve + +$${dy \over dx} = {{dy \over dt} \over {dx \over dt}} \> \vert \> {dx \over dt} \ne 0$$ + +$${d^2 \over dx^2} = {d(y^\prime) \over dx} = {{dy^\prime \over dt} \over {dx \over dt}} \> \vert \> y^\prime = {dy \over dx}$$ + -- 2.43.2