Complex derivative involving exponents and natural log Find: (d)(dx) a^(x\ln x)

JetssheetaDumcb

JetssheetaDumcb

Answered question

2022-10-20

Complex derivative involving exponents and natural log
Find: d d x a x ln x
I have tried several methods involving u-substitution etc, but can't figure it out.

Answer & Explanation

Phoebe Medina

Phoebe Medina

Beginner2022-10-21Added 17 answers

d ( a x ln ( x ) ) d x = d ( a x ln ( x ) ) d ( x ln ( x ) ) ( ln ( x ) + 1 ) = ln ( a ) a x ln ( x ) ( ln ( x ) + 1 )
The last result is obtained by the logarithm laws and using the fact that a x = e x ln ( a ) , and this holds a 0 , a a ( x )
Keyla Koch

Keyla Koch

Beginner2022-10-22Added 3 answers

d d x a x ln x = d d x e x ln x ln a = ( d d x x ln x ln a ) e x ln x ln a = ln a ( d d x x ln x ) e x ln x ln a = ln a ( 1 + ln x ) e x ln x ln a = ln a ( 1 + ln x ) a x ln x

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