What Is the Correct Derivative of the Function p(t)?

[saadsarfraz]

Homework Statement

Hi can anyone tell me what is the derivative of this function.

Homework Equations

p(t) = u(X(t), t) The derivative of p with respect to t

The Attempt at a Solution

dp/dt = du/dX * dX/dt + 1 ?? or is it going to be du/dX * dX/dt

 

[fzero]

You are almost right, but you need to use some partial derivatives:

$$\frac{dp}{dt} = \frac{\partial u}{\partial X} \frac{dX}{dt} + \frac{\partial u}{\partial t}.$$

 

[saadsarfraz]

thank you