Using Chain Rule to Find du/dT & du/dv: Step-by-Step Guide

[sphyics]

If a function is given by u = u(T,v) how to use the chain rule to write how u changes with respect to T & v.
Please specify the steps involved.
i understand chain rule as $\frac{du}{dx}$ = $\frac{du}{dy}$ $\frac{dy}{dx}$

 

[mathman]

Assuming T and v are both functions of x, the chain rule gives:
du/dx = (∂u/∂T)(dT/dx) + (∂u/∂v)(dv/dx)

 

[sphyics]

Assuming T and v are both functions of x, the chain rule gives:
du/dx = (∂u/∂T)(dT/dx) + (∂u/∂v)(dv/dx)

very much thanks for ur quick response :)

how does the symbol ∂ differs in meaning with d

 

[JHamm]

$\partial$ (read "partial") is basically the equivalent of $d$ in multivariable calculus, it means you take the derivative of a function with respect to a variable while considering all other variables as constants during that operation.

For example if I have
$$F = x^2 + 2xy + \frac{x}{y}$$
Then
$$\frac{\partial F}{\partial x} = 2x + 2y + \frac{1}{y}$$
Can you find $\frac{\partial F}{\partial y}$? :)

 

[sphyics]

[itex] Can you find $\frac{\partial F}{\partial y}$? :)[/itex]

$<br /> = 2x - x/y²<br /> <br /> i think that's the right answer :)$

 

[JHamm]

I think so too :)

 

[sphyics]

Appreciate ur help :)