Differentiate the function. y=\ln(e^{-x}+xe^{-x})

tornesasln

tornesasln

Answered question

2021-11-14

Differentiate the function. y=ln(ex+xex)

Answer & Explanation

Archie Griffin

Archie Griffin

Beginner2021-11-15Added 9 answers

Use the log properties to simplify.
ln(ex+xex)
factoring pattern: a+ab=a(1+b)
=ln[ex(1+x)]
(logbu+logbv=logb(uv))
=lnex+ln(1+x)
=(x)lne+ln(1+x)
=(x)(1)+ln(1+x)
=x+ln(1+x)
The ln derivative formula: (lnu)=(uu)
Differentiate
y=1+(1+x)1+x=1+11+x
=1x+11+x
=x1+x

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?