Calculate the 4th power of (- the 2nd power of XY and the 3rd power of Z)

Calculate the 4th power of (- the 2nd power of XY and the 3rd power of Z)

Original formula = (- 1) to the 4th power X to the 4th power y (2) × 4) Power Z (3) × 4) Power
=The 4th power of X, the 8th power of Y and the 12th power of Z
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Find the mixed differential of binary function z = f (x ²- y ², Find ∂ to the XY power of E ² z/∂x∂y

Known binary function z = f [x ²- y ², E ^ (XY)] find ∂ ² z/∂x∂y
Let z = f (U, V), u = X ²- y ², v=e^(xy)；
∂z/∂x=(∂z/∂u)(∂u/∂x)+(∂z/∂v)(∂v/∂x)=(∂z/∂u)(2x)+(∂z/∂v)[ye^(xy)]
∂ ² z/∂x∂y=2x(∂ ² z/∂u ²) (∂u/∂y)+ye^(xy)(∂ ² z/∂v ²) (∂v/∂y)+(∂z/∂v)[e^(xy)+xye^(xy)]
=-4xy(∂ ² z/∂u ²)+ ye^(xy)(∂ ² z/∂v ²) [xe^(xy)]+(∂z/∂v)[e^(xy)+xye^(xy)]
=-4xy(∂ ² z/∂u ²)+ xye^(2xy)(∂ ² z/∂v ²)+ [e^(xy)+xye^(xy)](∂z/∂v).

Known x ²+ 4y-2x + 8y + 5 = 0, find (the fourth power of X - the fourth power of Y) / (2x) ²+ xy-y ²）× （2x-y)/（xy-y ²） ÷ 〔（x ²+ y ²）/ （y）〕 ² Value of

X ^ 2 + 4Y ^ 2-2x + 8y + 5 = 0 bar (x-1) ^ 2 + 4 (y + 1) ^ 2 = 0x = 1, y = - 1 (the fourth power of X - the fourth power of Y) / (2x) ²+ xy-y ²）× （2x-y)/（xy-y ²） ÷ 〔（x ²+ y ²）/ （y）〕 ²= (1^4-(-1)^4)/（2x ²+ xy-y ²）× （2x-...

Given x + y = 6 and xy = 4 (1), find X ²+ y ² 2) Find (X-Y) ² 3) Find the fourth power of X + the fourth power of Y

x ²+ y ² = (x+y) ²- 2xy=6 ²- 8=28（x-y） ²= x ²+ y ²- 2XY = 28-8 = 20x quartic + y quartic = (x) ²+ y ²)²- 2x ² y ²= twenty-eight ²- 2*4 ²= seven hundred and fifty-two

X-Y = - 1, xy = 3. X to the power of 3, y-2x ² y ²+ The value of the third power of XY

Original formula = XY (x) ²- 2xy+y ²)
=xy(x-y) ²
=3 × (-1) ²
=3

Find the mixed integral of binary function z = f (x ²- y ², XY power of E)

Find the total differential of binary function z = f [x ²- y ², E ^ (XY)] let z = f (U, V), u = X ²- y ², V = e ^ (XY), then DZ = (∂ f / ∂ U) DU + (∂ f / ∂ V) DV. (1) where Du = (∂ U / ∂ x) DX + (∂ U / ∂ y) dy = 2xdx-2ydy; dv=(&...