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Find the partial derivatives of the following functions
a) z = 8x^2 − 4xy + 5y^2
b) z = 5xe^y
c) z = 3xln(y)

Sagot :

caylus

Answer:

Hello,

Step-by-step explanation:

a)

[tex]z=8x^2-4xy+5y^2\\\\\dfrac{\partial z}{\partial x} =16x^2-4y\\\\\dfrac{\partial z}{\partial y} =-4x+10y\\[/tex]

b)

[tex]z=5xe^{y}\\\\\dfrac{\partial z}{\partial x} =5e^y\\\\\dfrac{\partial z}{\partial y} =5xe^y\\[/tex]

c)

[tex]z=3xln(y)\\\\\dfrac{\partial z}{\partial x} =3ln(y)\\\\\dfrac{\partial z}{\partial y} =\dfrac{3x}{y}\\[/tex]

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