Use logarithmic differentiation to find (dy)/(dx) for the following function. y=(x-2)^(x+1)

criminauiac

criminauiac

Answered question

2022-12-18

Use logarithmic differentiation to find d y d x for the following function
y = ( x 2 ) x + 1

Answer & Explanation

utisnutuga3

utisnutuga3

Beginner2022-12-19Added 5 answers

y = ( x 2 ) x + 1
We take in on borh sides
ln y = ln ( x 2 ) x + 1 ln y = ( x + 1 ) ln ( x 2 )
implicit diff w.r.t - x 2
1 y d y d x = ( x + 1 ) d d x ( ln ( x 2 ) ) + ln ( x 2 ) d d x ( x + 1 ) = ( x + 1 ) 1 x 2 + ln ( x 2 ) 1 d y d x = y [ x + 1 x + 2 + ln ( x 2 ) ] y = ( x 2 ) x + 1 [ x + 1 x 2 + ln ( x 2 ) ]

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