Answer the following (internal choice): a

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

Problem

Answer the following (internal choice): a. If 1−x2+1−y2=a(x−y)\sqrt{1-x^2} + \sqrt{1-y^2} = a(x-y) , then prove that dydx=1−y21−x2\frac{dy}{dx} = \sqrt{\frac{1-y^2}{1-x^2}} . b. If x=a(cos⁡θ+log⁡tan⁡θ2)x = a \left( \cos \theta + \log \tan \frac{\theta}{2} \right) and y=sin⁡θy = \sin \theta , then find d2ydx2\frac{d^2 y}{dx^2} at θ=π4\theta = \frac{\pi}{4} .

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