Difference between revisions of "Math 22 Chain Rule"
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| − | + | ==The Chain Rule== | |
| + | If <math>y=f(x)</math> is a differentiable function of <math>u</math> and <math>u=g(x)</math> is a | ||
| + | differentiable function of <math>x</math>, then <math>y=f(g(x))</math> is a differentiable function | ||
| + | of <math>x</math> and | ||
| + | |||
| + | <math>\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}</math> | ||
| + | |||
| + | In another word, <math>\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)</math> | ||
[[Math_22| '''Return to Topics Page''']] | [[Math_22| '''Return to Topics Page''']] | ||
'''This page were made by [[Contributors|Tri Phan]]''' | '''This page were made by [[Contributors|Tri Phan]]''' | ||
Revision as of 05:58, 23 July 2020
The Chain Rule
If Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=f(x)}
is a differentiable function of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle u}
and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle u=g(x)}
is a
differentiable function of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x}
, then Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=f(g(x))}
is a differentiable function
of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x}
and
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}}
In another word,
![{\displaystyle {\frac {d}{dx}}[f(g(x))]=f'(g(x))\cdot g'(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0fe337c7649f42de72e6de2b1ef3d88949b95f90)
This page were made by Tri Phan