Use logarithmic differentiation to find the derivative of the function. y=(tan(x))^(9/x)

Jaylene Hunter

Jaylene Hunter

Answered question

2022-07-16

Use logarithmic differentiation to find the derivative of the function.
y = ( tan ( x ) ) 9 x

Answer & Explanation

penangrl

penangrl

Beginner2022-07-17Added 17 answers

y = ( tan ( x ) ) 9 x
Apply ln on both sides
ln y = ln ( tan x ) 9 x = 9 x ln ( tan ( x ) )
Apply derivative on both sides
d d x ln y = 9 d d x ln ( tan x ) x 1 y d y d x = 9 [ x d d x ln ( tan x ) ln ( tan x ) d d x x x 2 ] ;  Quotient Rule d y d x = 9 y [ x 1 tan x sec 2 x ln ( tan x ) x 2 ]
Since y = ( tan x ) 9 x
d x d y = 9 ( tan x ) 9 x [ x sec 2 tan x sec 2 x ln ( tan x ) x 2 ]
d y d x = 9 ( tan x ) 9 x [ sec 2 x tan x sec 2 x 1 x 2 ln ( tan x ) ]

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