partial derivative of 2/x

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∂∂x (2x )=−2x²

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∂ ∂ x (2x )=−2x²

steps

∂ ∂ x (2x )

Take the constant out: (a·f)′=a·f ′
=2∂ ∂ x (1x )

Apply exponent rule: 1a =a⁻¹
=2∂ ∂ x (x⁻¹)

Apply the Power Rule: ddx (x^a)=a·x^a−1
=2(−1· x⁻¹⁻¹)

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Simplify 2(−1· x⁻¹⁻¹): −2x²
=−2x²