# Partial Derivative / Multivariable Chain Rule Notation

Example 1.

w = $x^2 +y^2 + z^2$

x = $uv$

y = $ucos(v)$

z = $usin(v)$

Using chain rule, find $\frac{∂w}{∂u}$

I understand partial derivatives and how to take chain rule for multivariable functions but why does $\frac{∂w}{∂u}$imply the same meaning as $\frac{∂w∘f}{∂u}$ where$f(u,v) = (x,y,z)$

• What is g and f ? Nov 10, 2017 at 2:33
• sorry edited... Nov 10, 2017 at 2:34

Because when you write “w” (and implicitly are thinking of x, y and z as functions of u and v) you are already thinking of $$w \circ f$$. No difference between the two.