If and , then prove that…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

x^2 + y^2 = t^{-1}

and

x^4 + y^4 = t^2 + \frac{1}{t^2}

, then prove that

\frac{dy}{dx} = \frac{1}{x^3 y}

Related theory

Algebraic Manipulation
Advanced Differentiation
Implicit and parametric differentiation
Derivatives of implicit functions
Continuity and Differentiability

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