Maclaurin series of tan (e^x -1)

[delsoo]

Homework Statement

for this, my coefficient of x^4 which is 8/4! = 1/3 .. but the ans should be 13/24... can you tell me which part contain mistake?
https://i.imgur.com/05NnrdM.jpg
https://i.imgur.com/28Q9o51.jpg

Homework Equations

The Attempt at a Solution

 

[Dick]

Homework Statement

for this, my coefficient of x^4 which is 8/4! = 1/3 .. but the ans should be 13/24... can you tell me which part contain mistake?
https://i.imgur.com/05NnrdM.jpg
https://i.imgur.com/28Q9o51.jpg

Homework Equations

The Attempt at a Solution

In your expression for the third derivative you didn't differentiate the dy/dx factor. You've only got part of the product rule there.

 

[delsoo]

i redo the question, now my coeffiecient of x becomes only 11 but not 13, now which part is wrong?
https://www.flickr.com/photos/123101228@N03/13809331763/

 

[Dick]

i redo the question, now my coeffiecient of x becomes only 11 but not 13, now which part is wrong?
https://www.flickr.com/photos/123101228@N03/13809331763/

Exactly the same sort of problem. You left out half of a product rule again. Can't YOU find it? You should have four [...] expressions, not three.

 

[delsoo]

sorry i really can't find it, i have 2 [ ... ] for d3y/dx3 , and i have 4 [...] for d4y/dx4 , can you be more specifiec telling me which part is wrong? thanks!

 

[delsoo]

..

...

 

[Dick]

sorry i really can't find it, i have 2 [ ... ] for d3y/dx3 , and i have 4 [...] for d4y/dx4 , can you be more specifiec telling me which part is wrong? thanks!

That's the problem. Yes, you should have four [...]'s for d4y/dx4. In the image you sent, you don't have four. You have three. You are missing one.

 

[delsoo]

That's the problem. Yes, you should have four [...]'s for d4y/dx4. In the image you sent, you don't have four. You have three. You are missing one.

thanks a lot! i found out i my grave mistake finally!