Question
$$\begin{aligned}&\text { If } f(x, y, z)=4 x^{2}+2 y^{3}+5 z^{5}+3 x-2 y+11 z+12, \text { find }\\&f_{x}(1,-2,-1), f_{y}(1,-2,-1), \text { and } f_{z}(1,-2,-1)\end{aligned}$$
Step 1
From the previous problem, we know that the partial derivatives are: $$f_{x}(x, y, z) = 8x + 3$$ $$f_{y}(x, y, z) = 6y^{2} - 2$$ $$f_{z}(x, y, z) = 25z^{4} + 11$$ Show more…
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For $f(x, y, z)=4 x^{3} y^{2} z^{2}+4 x^{2}+2 y^{3}+5 z^{5}+3 x-2 y+11 z+12$ find $f_{x z y}(x, y, z)$ and $f_{x y z}(x, y, z)$.
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$$\begin{aligned} &\text { For } f(x, y, z)=2 x^{3} y^{2} z^{2}+2 x^{2}+2 y^{2}+3 z^{2}+2 x y+3 x z+5 y z-2 x+\\ &2 y+2 z, \text { find } f_{z x y}(x, y, z) \text { and } f_{x z y}(x, y, z) \end{aligned}$$
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