From: Andrew Lorimer Date: Wed, 15 Aug 2018 02:52:57 +0000 (+1000) Subject: product & quotient rules X-Git-Tag: yr11~68 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/e8484a6184f60482db41328469475f99e6fd44ff?hp=13991b8583b976248f9ea95d353010c8fe2ccd81 product & quotient rules --- diff --git a/spec/calculus.md b/spec/calculus.md index 503b191..c0056c4 100644 --- a/spec/calculus.md +++ b/spec/calculus.md @@ -109,3 +109,17 @@ ${dy \over du} = 7u^6$ $7u^6 \times$ +## Product rule + +If $f(x)=u(x) \times v(x)$, then $f^\prime (x) = u(x) \times v^\prime(x) + v(x)\times u^\prime(x)$ + +If $y=uv$, then derivative ${dy \over dx} = u{dv \over dx} + v{du \over dx}$ + +Surds can be left on denomintaors. + +## Quotient rule + +If $f(x)={u(x) \over v(x)}$, then $f^\prime(x)={{v(x)u^\prime(x)-u(x)v^\prime(x)} \over [v(x)]^2}$ + +If $y={u(x) \over v(x)}$, then derivative ${dy \over dx} = {{v{du \over dx} - u{dv \over dx}} \over v^2}$ +