Let . Evaluate at…

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

Problem

Let y=(sin⁡x1+cos⁡x)tan⁡xy=\left(\dfrac{\sin x}{1+\cos x}\right)^{\tan x}. Evaluate y′y' at x=π4x=\dfrac{\pi}{4}. (a) (2−1)[2ln⁡(2−1)+22](\sqrt2-1)[2\ln(\sqrt2-1)+2\sqrt2] (b) (2−1)[ln⁡(2−1)+2](\sqrt2-1)[\ln(\sqrt2-1)+\sqrt2] (c) (2−1)[2ln⁡(2−1)+2](\sqrt2-1)[2\ln(\sqrt2-1)+\sqrt2] (d) (2−1)[2ln⁡(2+1)+2](\sqrt2-1)[2\ln(\sqrt2+1)+\sqrt2]

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