If y = [(tan x) to the power tan x] to the power tan x, find dy/dx at x = pie/4

Asked by pratikbharadia | 30th Dec, 2009, 10:39: AM

Expert Answer:

tan π/4 = 1

and log 1 = 0

sec π/4 = 1/cos π/4 = 2

y = ((tanx)tanx)tanx

Take log on both sides,

log y = tan2x log tanx

Differentiating both sides,

(1/y)(dy/dx) =tan2x (1/tanx) sec2x + 2tanx sec2x log tanx

dy/dx =(tan2x (1/tanx) sec2x + 2tanx sec2x log tanx)y

dy/dx =(tan2x (1/tanx) sec2x + 2tanx sec2x log tanx)((tanx)tanx)tanx

Put x = π/4

dy/dx = 2

Regards,

Team,

TopperLearning.

 

Answered by  | 30th Dec, 2009, 02:02: PM

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