(\partial}{\partial z}(\frac{xy)/z)

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∂∂z (xyz )=−xyz²

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∂ ∂ z (xyz )=−xyz²

steps

∂ ∂ z (xyz )

Treat x, y as constants

Take the constant out: (a·f)′=a·f ′
=xy∂ ∂ z (1z )

Apply exponent rule: 1a =a⁻¹
=xy∂ ∂ z (z⁻¹)

Apply the Power Rule: ddx (x^a)=a·x^a−1
=xy(−1· z⁻¹⁻¹)

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Simplify xy(−1· z⁻¹⁻¹): −xyz²
=−xyz²