Chain rule with 2nd Partials

1. Oct 11, 2009

rabbleguy

We have f(x(y,z),t(y,z)).

This is more of a study question. I don't know how to expand out $$d^{2}f/dz^2$$

I know df/dz = df/dx*dx/dz + df/dt*dt/dz, but I don't know how to expand this to the 2nd derivative. I think the product rule comes in to play? Not really sure.

Thanks for your help.

2. Oct 11, 2009

LCKurtz

Using the more convenient subscript notation, you have used:

fz = fxxz+ fttz

Now you have to do the same thing to this expression, which can be done termwise:

fzz =(fxxz)x$\cdot\,$xz + (fxxz)t$\cdot\,$tz

and, yes, you will need the product rule inside those parentheses.

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