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What is the derivative of #x^(tan x)#?

1 Answer

Jun 26, 2016

# y' = x^(tan x)(sec^2 x ln x + tan x/x)#

Explanation:

#y = x^(tan x)#
#ln y = ln x^(tan x) = tanx ln x#
#1/y y' =( tanx ln x)'#

#1/y y' = sec^2 x ln x + tan x (1/x)# by the product rule

# y' = y(sec^2 x ln x + tan x (1/x))#

# y' = x^(tan x)(sec^2 x ln x + tan x/x)#

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