The ellipse is given

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

Problem

The ellipse 4x2+9y2=364x^{2}+9y^{2}=36 is given. Show that d2ydx2=−4(9y2+4x2)81y3.\frac{d^{2}y}{dx^{2}}=-\frac{4\bigl(9y^{2}+4x^{2}\bigr)}{81y^{3}}.

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