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Implicit Differentiation

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If ln⁡(sin⁡y)+x3=2\ln(\sin y) + x^3 = 2, then dydx=\frac{dy}{dx} =

A

dydx=−3x2sin⁡y\displaystyle\frac{dy}{dx} = -\frac{3x^2}{\sin y}

B

dydx=−3x2tan⁡y\displaystyle\frac{dy}{dx} = -3x^2 \tan y

C

dydx=−3x2cot⁡y\displaystyle\frac{dy}{dx} = -3x^2 \cot y

D

dydx=3x2tan⁡y\displaystyle\frac{dy}{dx} = 3x^2 \tan y

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