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Hi help rn plss this is a system of equations question

Mathematics

1 answer:

otez555 [7]2 years ago

8 0

Answer:

x=6, y=2

Step-by-step explanation:

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Find the differential of the function w=xsin(2yz^4).

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The differential of

$w = x \sin(2yz^4)$

$\mathrm dw = \dfrac{\partial w}{\partial x}\,\mathrm dx + \dfrac{\partial w}{\partial y}\,\mathrm dy + \dfrac{\partial w}{\partial z}\,\mathrm dz$

where the partial derivatives are

$\dfrac{\partial w}{\partial x} = \sin(2yz^4) \\\\ \dfrac{\partial w}{\partial y} = x \cos(2yz^4) \times 2z^4 = 2xz^4 \cos(2yz^4) \\\\ \dfrac{\partial w}{\partial z} = x \cos(2yz^4) \times 8yz^3 = 8xyz^3 \cos(2yz^4)$

So the differential dw is

$\mathrm dw = \boxed{\sin(2yz^4)}\,\mathrm dx + \boxed{2xz^4 \cos(2yz^4)}\,\mathrm dy + \boxed{8xyz^3 \cos(2yz^4)}\,\mathrm dz$

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