Find all nine of the second order partial derivatives of f H

Find all nine of the second order partial derivatives of f.

How many third order partial derivatives of ff are there? Do not compute the third order partial derivatives, just answer how many of them there are.

fx = e^y + 2xz

fy = xe^y - sin(z)

fz = -ycos(z) + x^2

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2nd order partials :
fxx = partial der of fx with x
So, fxx = 2z

fyy = xe^y

fzz = ysin(z)

fxy = d/dy(e^y + 2xz) = e^y

fxz = d/dz(e^y + 2xz) = 2x

fyx = d/dx(xe^y - sinz)= e^y

fyz = d/dz(xe^y - sinz) = -cos(z)

fzx = d/dx(-ycos(z) + x^2) = 2x

fzy = d/dy(-ycos(z) + x^2) = -cos(z)

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3)
First order , we had 3

Second order derivatives, we had 3^2 = 9

Third order derivatives, we\'d have 3^3 = 27

So, we\'d have 27 third order derivatives