- #1

- 685

- 4

## Main Question or Discussion Point

Se a function f(x(t, s), y(t, s)) have as derivative with respect to t:

[tex]\frac{df}{dt}=\frac{df}{dx} \frac{dx}{dt}+\frac{df}{dy} \frac{dy}{dt}[/tex]

And, with respect to s:

[tex]\frac{df}{ds}=\frac{df}{dx} \frac{dx}{ds}+\frac{df}{dy} \frac{dy}{ds}[/tex]

But, how will be the derivative with respect to t and s?

[tex]\frac{d^2f}{dtds}[/tex]

Or with respect to s and t

[tex]\frac{d^2f}{dsdt}[/tex]

I don't know if there is difference when change the order between t and s...

[tex]\frac{df}{dt}=\frac{df}{dx} \frac{dx}{dt}+\frac{df}{dy} \frac{dy}{dt}[/tex]

And, with respect to s:

[tex]\frac{df}{ds}=\frac{df}{dx} \frac{dx}{ds}+\frac{df}{dy} \frac{dy}{ds}[/tex]

But, how will be the derivative with respect to t and s?

[tex]\frac{d^2f}{dtds}[/tex]

Or with respect to s and t

[tex]\frac{d^2f}{dsdt}[/tex]

I don't know if there is difference when change the order between t and s...