Derivative of Composite Function/Also presented as

From ProofWiki
Jump to navigation Jump to search

Derivative of Composite Function: Also presented as

The Derivative of Composite Function is also often seen presented using Leibniz's notation for derivatives:

$\dfrac {\d y} {\d x} = \dfrac {\d y} {\d u} \cdot \dfrac {\d u} {\d x}$

or:

$\dfrac \d {\d x} \map u v = \dfrac {\d u} {\d v} \cdot \dfrac {\d v} {\d x}$

where $\dfrac {\d y} {\d x}$ denotes the derivative of $y$ with respect to $x$.


Some sources go so far as to mix their notation and present something like this:

$y' = \dfrac {\d f} {\d g} \map {g'} x$


Also to be mentioned is:

$D_x^1 w = D_u^1 w \, D_x^1 u$

where ${D_x}^k u$ denotes the $k$th derivative of $u$ with respect to $x$.


Sources

Retrieved from "https://proofwiki.org/w/index.php?title=Derivative_of_Composite_Function/Also_presented_as&oldid=684157"