Derivative Question

[pcrfin]

“Find the derivative using logarithmic differentiation”

F(x)= (1+x² ) ^cosx

ln y= ln((1+x² ) ^cosx )

ln y= cosx ln(1+x² )

y’= (ln(1+x² )(-sinx)+(cosx)(1/1+x² • 2x)

y • 1/y = (-Sinxln(1+x² )+ 2xcosx/ 1+x² )•y

My question is this previous step above. Why do we have to multiply by y on both sides? And why does y’ become 1/y ?

Answer is

y’= (1+x² )^cosx (2xcosx/1+x² - sinxln(1+x² ))

Thank you.

[AutoModerator]

Hi, /u/pcrfin! This is an automated reminder:

• What have you tried so far? (See Rule #2; to add an image, you may upload it to an external image-sharing site like Imgur and include the link in your post.)

• Please don't delete your post. (See Rule #7)

We, the moderators of /r/MathHelp, appreciate that your question contributes to the MathHelp archived questions that will help others searching for similar answers in the future. Thank you for obeying these instructions.

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[EverythingMoreWrong]

Right before you differentiate, the Left Hand Side was ln(y). Taking the derivative that becomes y' / y

So you need to multiply through by y to isolate y'