Turn on thread page Beta
 You are Here: Home >< Maths

# Simple P5 differentiation problem. watch

1. I'm differentiating a function and get an answer different to that in the book. Can anyone clarify whether i'm right or wrong? Thanks.

Differentiate artanh(x^2)

y=artanh(x^2)
tanhy = x^2
(sechy)^2 (dy/dx) = 2x

cosh^2(y) - sinh^2(y) = 1
1 - tan^2(y) = sech^2(y)
1 - (x^2)^2 = sech^2(y)
(1-x^4) dy/dx = 2x
dy/dx = 2x/(1-x^4)

However. The book gives 2x/(1-x^2)
Where does the mistake lie? Thanks.
2. i get ur answer as well using a different method
Attached Images

3. err... differentiate arctan x = 1 / (1+x^2)... standard derivative... look up the integrating section and use it in reverse in the formula book

by chain rule... y = arctan u, u = x^2
so.. y' = 1 / (1+u^2).... u' = 2x

so by chain rule... derivative = y' * u' = 2x / (1+x^4)
4. Thanks for the confirmation. Glad to know the book is wrong rather than myself.
I agree that i could have used the chain rule but i'm trying to familiarise myself with how the results are derived as much as possible, rather than relying on the formulae.
Thanks again.

Edit: Would it be possible to finish P5 within a week?
5. (Original post by Gaz031)
Thanks for the confirmation. Glad to know the book is wrong rather than myself.
I agree that i could have used the chain rule but i'm trying to familiarise myself with how the results are derived as much as possible, rather than relying on the formulae.
Thanks again.

Edit: Would it be possible to finish P5 within a week?
I'm going to start P5 on Tuesday. If I finish it in a couple of months I'll be pleased enough!

Aitch
6. (Original post by Gaz031)
Edit: Would it be possible to finish P5 within a week?
Yes, it is. You just need to work really hard.
7. Just finishing the differentiation chapter. Hope to complete the chapter and start integration by tonight.
If i have to start Biology coursework this week i will have to forget about P5 for a while though.
8. Now i'm trying to trying to integrate sech2x with respect to x.
I get the answer 0.5arctan(sinh2x) + C but the book gets arctan(e^2x). Are these answers equivelant? If so how do you get from one to the other?
9. I believe your answer's right, it's only a constant away from arctan(e^2x).

This is just a guess, but I think the book wrote out sech2x in terms of e^x and integrated.

Turn on thread page Beta
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 30, 2005
Today on TSR

### The TSR A-level options discussion thread

Choosing A-levels is hard... we're here to help

### University open days

• Heriot-Watt University
School of Textiles and Design Undergraduate
Fri, 16 Nov '18
• University of Roehampton
All departments Undergraduate
Sat, 17 Nov '18
• Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 17 Nov '18
Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.