Prove the following. i) If y=axax...∞, then prove that dydx=y2logyx( – InterviewSolution

1.	Prove the following. i) If y=axax...∞, then prove that dydx=y2logyx(1−ylogxlogy) ii) If y=cosxcosxcosxcosx...∞, then prove that dydx=−y2tanx1−ylogcosx
Answer» Prove the following. i) If $y = a^{x^{a^{x^{.^{.^{.^{\infty}}}}}}}$ , then prove that $\frac{d y}{d x} = \frac{y^{2} log y}{x (1 - y log x log y)}$ ii) If $y = cos x^{cos x^{cos x^{cos x^{.^{.^{.^{\infty}}}}}}}$ , then prove that $\frac{d y}{d x} = \frac{- y^{2} tan x}{1 - y log cos x}$

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