CBSE Class 12-science Answered
If y = [(tan x) to the power tan x] to the power tan x, find dy/dx at x = pie/4
Asked by pratikbharadia | 30 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 | 30 Dec, 2009, 02:02: PM
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