Continuity and DifferentiabilityMedium
Question
The derivative of (tan x)x is equal to -
Options
A.x(tan x)x-1
B.(tan x)x [sec x + tan x]
C.(tan x)x [xsec x cosec x + log tan x]
D.(tan x)x [sec2x + xtan x]
Solution
y = (tan x)x
= (variable) variable
y = (tan x)x
log y = x log tan x
= log tan x + 
× sec2x
= y [log tan x + x sec x cosec x]
= (tan x)x [log tan x + x sec x cosec x]
= (variable) variable
y = (tan x)x
log y = x log tan x
= log tan x + × sec2x = y [log tan x + x sec x cosec x] = (tan x)x [log tan x + x sec x cosec x]Create a free account to view solution
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