Not understanding these manipulations involving Partial Derivatives

MatinSAR
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Homework Statement
Find partial derivatives
Relevant Equations
dy/dx=(dy/dt)(dt/dx)
Can someone please help me to find out what happened here ?

1675445974557.png
 
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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
$$\partial f(u,v) / \partial t = (\partial f/ \partial u) (\partial u/ \partial t) + (\partial f/ \partial v) (\partial v/ \partial t)$$
 
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ergospherical said:
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 🙏🙏
 

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