Given the implicit equation

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

Problem

Given the implicit equation (csc⁡y)2+xy=4(\csc y)^{2}+x y=4, find dydx\dfrac{dy}{dx} in terms of xx and yy. (a) −yx+2csc⁡2ycot⁡y-\dfrac{y}{x+2\csc^{2} y\cot y} (b) −yx−2csc⁡2ycot⁡y-\dfrac{y}{x-2\csc^{2} y\cot y} (c) yx−2csc⁡2ycot⁡y\dfrac{y}{x-2\csc^{2} y\cot y} (d) −yx−csc⁡2ycot⁡y-\dfrac{y}{x-\csc^{2} y\cot y}

Related theory

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