Question: If $y = (\tan x)^{(\tan x)^{\tan x}}$, then \(\frac{dy}{dx}\left| \begin{aligned} & \\ & x = \pi...

Question

If $y = (\tan x)^{(\tan x)^{\tan x}}$ , then $\frac{dy}{dx}\left| \begin{aligned} & \\ & x = \pi/4 \end{aligned} \right.\$ =

Answer 1

log y = (tan x)^{tan x} log tan x

log(log y) = tan x log tan x + log (log tan x)

$\frac{1}{y\log y}\frac{dy}{dx}$ = sec²x log tan x + sec²x + $\frac{1}{{logtan}x}.\frac{1}{\tan x}$ sec²x

does not exist at x = π/4 because log tan π/4 = 0

Question: If \(y = (\tan x)^{(\tan x)^{\tan x}}\), then \(\frac{dy}{dx}\left| \begin{aligned} & \\ & x = \pi...