Gradients - composition | MIT 18.02SC Multivariable Calculus, Fall 2010

Gradients - composition
Instructor: David Jordan
View the complete course: ocw.mit.edu/18-...
License: Creative Commons BY-NC-SA
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[@omaraymanbakr3664]

Drawing the dependency graph between variables will make this problem trivial.
f
/ \ \
x y z
/\
x z
with g= f ( x,z), you have to calculate partial derv. w.r.t x and z.

[@ricardo4fun922]

This part of the course is very confusing.

[@jeffreyanderson5333]

This part is the juice of this course.

[@jaepark8475]

same

[@seungchullee221]

I think knowing DAG in graph theory is very helpful(inevitable?) to apply chain rule to composition of functions.

[@middlevoids]

Because it's a new material to me i write it like this (using the chain rule):
gx or dg/dx (means fixed z) = df/dx*dx/dx + df/dy*dy/dx + df/dz*dz/dx
The same but for gy.
From the constraint i find dy/dx and dy/dz respectively