- #1

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## Homework Statement:

- If u = f(x,y) and x=x(t) and y=y(t) then find the 2nd total derivative of u with respect to t

## Relevant Equations:

- chain rule

du/dt = (∂f/∂x)(dx/dt) + (∂f/∂y)(dy/dt)

So i write the operator as

d/dt = (dx/dt)(∂/∂x) + (dy/dt)(∂/∂y) and apply it to du/dt ; in the operator it is the partial derivative that acts on du/dt which involves using the product rule.

I am having a problem with the term involving (∂/∂x) (dx/dt) ; dx/dt is a function of t only so i can't figure out what the partial derivative is

So i write the operator as

d/dt = (dx/dt)(∂/∂x) + (dy/dt)(∂/∂y) and apply it to du/dt ; in the operator it is the partial derivative that acts on du/dt which involves using the product rule.

I am having a problem with the term involving (∂/∂x) (dx/dt) ; dx/dt is a function of t only so i can't figure out what the partial derivative is