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Looking for help regarding following question:

Being $f(x,y,z) = e^{xyz}$, find the function partial derivatives sum related to each variable on $P(1,0,1)$ point.

Wouldn't anyone answer?

Ernie060
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Renan41
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    @Renen41 Do you know how to compute partial derivatives? If you don't, you must learn to do that before hand... If you do, compute them, add them up and substitute $x=1, y=0, z=1$ in the end. – PierreCarre Oct 12 '20 at 15:59

1 Answers1

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Managed as follows:

Being $ f = e^{u}$ and $u = xyz$, as $\frac{df(u)}{dx}=\frac{df}{du}\times \frac{du}{dx}$, do:

$f(x,y,z) = e^{xyz}$ at $P(1,0,1)$

$\frac{\partial f}{\partial x} e^{xyz} = e^{xyz} \times yz = e^{1 \times 0 \times 1} \times 0 \times 1 = 0$

$\frac{\partial f}{\partial y} e^{xyz} = e^{xyz} \times xz = e^{1 \times 0 \times 1} \times 1 \times 1 = 1$

$\frac{\partial f}{\partial z} e^{xyz} = e^{xyz} \times xz = e^{1 \times 0 \times 1} \times 1 \times 0 = 0$

Finally , $0 + 1 + 0 = 1$

Rubem74
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