Given a function f(x(t, s) y(t, s)), if is possible to compact(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{∂f}{∂t}=\frac{∂f}{∂x} \frac{∂x}{∂t}+\frac{∂f}{∂y} \frac{∂y}{∂t}[/tex]

by

[tex]\frac{df}{dt}=\bigtriangledown f\cdot \frac{d\vec{r}}{dt}[/tex]

So, analogously, isn't possible to compact the sencond derivate

[tex]\frac{\partial^2 f}{\partial s \partial t} = \frac{\partial^2 f}{\partial x^2} \frac{\partial x}{\partial s }\frac{\partial x}{\partial t } + \frac{\partial^2 f}{\partial x \partial y}\left( \frac{\partial y}{\partial s }\frac{\partial x}{\partial t } + \frac{\partial x}{\partial s }\frac{\partial y}{\partial t }\right) + \frac{\partial^2 f}{\partial y^2} \frac{\partial y}{\partial s }\frac{\partial y}{\partial t }+\frac{\partial f}{\partial x}\frac{\partial^2 x}{\partial s \partial t}+\frac{\partial f}{\partial y}\frac{\partial^2 y}{\partial s \partial t}[/tex]

using matrix with the matrix Hessian(f) ?

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# Second derivative and tensors

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