How Should Derivatives in Multivariable Chain Rules Be Notated?

[hojoon yang]

Hi

I understood above differential

## typo. RHS= 2*f ' (x,2z-x)

but, what is answer of below equation?

is this right?

f ' ( g(z),2z-x) * g' (z) + f ' ( g(z),2z-x) *2

 

[S.G. Janssens]

Hi

I understood above differential

## typo. RHS= 2*f ' (x,2z-x)

This notation is ambiguous, because it is not clear whether you differentiate $f$ w.r.t. the first or second variable. So I would write
$$
\frac{d}{dz} f(x, 2z - x) = 2 D_2f(x, 2z - x)
$$
instead. (There are other notations, but choose one that is clear.)

but, what is answer of below equation?

is this right?

f ' ( g(z),2z-x) * g' (z) + f ' ( g(z),2z-x) *2

Same comment as above. Change the first $f'$ to $D_1f$ and the second $f'$ to $D_2f$.