# I Chain rule in a multi-variable function

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1. May 7, 2016

### Ananthan9470

Suppose you have a parameterized muli-varied function of the from $F[x(t),y(t),\dot{x}(t),\dot{y}(t)]$ and asked to find $\frac{dF}{dt}$, is this the correct expression according to chain rule? I am confused because of the derivative terms involved.

$\frac{dF}{dt}=\frac{\partial F}{\partial x} \frac{dx}{dt} + \frac{\partial F}{\partial y} \frac{dy}{dt}$

Or similar terms containing $\dot{x}(t)$ etc should also be included or it is something else altogether?

2. May 7, 2016

### Staff: Mentor

If the function had parameters x, y, z, and w, the total derivative would have four terms, with the last two being $\frac{\partial F}{\partial z} \frac{dz}{dt} + \frac{\partial F}{\partial w} \frac{dw}{dt}$. I believe that the derivative you're trying to find needs similar terms, with the partials being with respect to $\dot{x}$ and $\dot{y}$.