# Simple P5 differentiation problem.

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#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.
0
15 years ago
#2
i get ur answer as well using a different method
0
15 years ago
#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)
0
#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?
0
15 years ago
#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
0
15 years ago
#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.
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#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.
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#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?
0
15 years ago
#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.
0
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