Not understanding these manipulations involving Partial Derivatives

[MatinSAR]

Homework Statement:

Find partial derivatives

Relevant Equations:

dy/dx=(dy/dt)(dt/dx)

Can someone please help me to find out what happened here ?

 

[ergospherical]

It's differentiating $f$ with respect to its arguments, then differentiating the arguments with respect to $t$. It might be clearer if you write $u = tx$ and $v=ty$, then
$$\partial f(u,v) / \partial t = (\partial f/ \partial u) (\partial u/ \partial t) + (\partial f/ \partial v) (\partial v/ \partial t)$$

 

[MatinSAR]

It's differentiating $f$ with respect to its arguments, then differentiating the arguments with respect to $t$. It might be clearer if you write $u = tx$ and $v=ty$, then
$$\partial f(u,v) / \partial t = (\partial f/ \partial u) (\partial u/ \partial t) + (\partial f/ \partial v) (\partial v/ \partial t)$$

That "tx" confused me ...
Now it's clear...
Thank you for your time 🙏🙏