- #1
MatinSAR
- 673
- 204
- Homework Statement
- Find partial derivatives
- Relevant Equations
- dy/dx=(dy/dt)(dt/dx)
Can someone please help me to find out what happened here ?
Not understanding these manipulations involving Partial Derivatives
- Thread starter MatinSAR
- Start date
Click For Summary
The discussion focuses on the process of differentiating a function f with respect to its arguments and then with respect to time t. A clarification is provided by substituting u = tx and v = ty, leading to the expression for the partial derivative of f with respect to t. This method illustrates how to apply the chain rule in the context of partial derivatives. The initial confusion regarding the notation "tx" is resolved through this explanation. Overall, the thread emphasizes the importance of understanding the chain rule in partial differentiation.
- #2
- 1,100
- 1,387
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
$$\partial f(u,v) / \partial t = (\partial f/ \partial u) (\partial u/ \partial t) + (\partial f/ \partial v) (\partial v/ \partial t)$$
$$\partial f(u,v) / \partial t = (\partial f/ \partial u) (\partial u/ \partial t) + (\partial f/ \partial v) (\partial v/ \partial t)$$
- #3
MatinSAR
- 673
- 204
That "tx" confused me ...ergospherical said:
Now it's clear...
Thank you for your time
