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)$

  • $\begingroup$ What is g and f ? $\endgroup$ Nov 10, 2017 at 2:33
  • $\begingroup$ sorry edited... $\endgroup$
    – mathguy
    Nov 10, 2017 at 2:34

1 Answer 1


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.


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