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When an alternating current passes through a series $R L C$ circuit, the voltage and current are out of phase by angle $\phi$ (see Section 12.7 ). Here $\phi=\tan ^{-1}\left[\left(X_{L}-X_{C}\right) / R\right],$ where $X_{L}$ and $X_{C}$ are the reactances of the inductor and capacitor, respectively, and $R$ is the resistance. Find $d \phi / d X_{C}$ for constant $X_{L}$ and $R.$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 3

Derivatives of the Inverse Trigonometric Functions

Derivatives

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