The Student Room Group

core 3 differentiation differentiate tan^2y pls help

ImageUploadedByStudent Room1447348480.994720.jpg pls help me with part a....I tried quotient rule but I'm still not getting the answer


Posted from TSR Mobile
Original post by bubblegumcat
ImageUploadedByStudent Room1447348480.994720.jpg pls help me with part a....I tried quotient rule but I'm still not getting the answer


Posted from TSR Mobile


Are you given the derivative of y = arctan(x)?
Are there any other rules of differentiation you can think of that may help?
Original post by SeanFM
Are you given the derivative of y = arctan(x)?


do I need to know that? I was never taught that :s


Posted from TSR Mobile
Original post by lukejoshjames
Are there any other rules of differentiation you can think of that may help?


I tried dy/du x du/dx(I think that's correct) and I got 2tanysec^2y but I'm not sure if that's right


Posted from TSR Mobile
Original post by bubblegumcat
do I need to know that? I was never taught that :s


Posted from TSR Mobile


Oh, don't worry about then :smile:

It may help to find dx/dy using the chain rule and see where that gets you.

Original post by bubblegumcat
I tried dy/du x du/dx(I think that's correct) and I got 2tanysec^2y but I'm not sure if that's right


Posted from TSR Mobile


There you go - so what does that equal to? And how do you get x back into the equation?
(edited 8 years ago)
Original post by SeanFM
Oh, don't worry about then :smile:

It may help to find dx/dy using the chain rule and see where that gets you.


oh i tried that I think...2tan y sec^2y is what I got..I'm not sure if that's correct?


Posted from TSR Mobile
Original post by bubblegumcat
oh i tried that I think...2tan y sec^2y is what I got..I'm not sure if that's correct?


Posted from TSR Mobile


Correct so far :borat: - now see my edit in the post above.
Reply 8
Original post by bubblegumcat
oh i tried that I think...2tan y sec^2y is what I got..I'm not sure if that's correct?


Posted from TSR Mobile


What trigonometric identity relates sec2y\sec^2 y and tan2y\tan^2 y?
Original post by Zacken
What trigonometric identity relates sec2y\sec^2 y and tan2y\tan^2 y?


1 +tan^2 = sec^2?


Posted from TSR Mobile
(edited 8 years ago)
Original post by SeanFM
Oh, don't worry about then :smile:

It may help to find dx/dy using the chain rule and see where that gets you.



There you go - so what does that equal to? And how do you get x back into the equation?


that would be 2tany/cos^2y right ?


Posted from TSR Mobile
Reply 11
Original post by bubblegumcat
1 +tan^2 = sec^2?


Posted from TSR Mobile


No. 1+tan2y=sec2y1 + \tan^2 y = \sec^2 y
Original post by Zacken
No. 1+tan2y=sec2y1 + \tan^2 y = \sec^2 y


how does that relate to this question? do I need to change tan^2y into sec^2y-1?


Posted from TSR Mobile
Original post by bubblegumcat
that would be 2tany/cos^2y right ?


Posted from TSR Mobile


That is still dx/dy but you've changed sec into cos, which can work but you don't need to do it.

Remember that dx/dy = 1/(dy/dx).

As Zacken is helping as well I will bow out. :hat2:
Reply 14
Original post by bubblegumcat
how does that relate to this question? do I need to change tan^2y into sec^2y-1?


Posted from TSR Mobile


No. You know that tan2y=x\tan^2 y = x and you want an answer involving xx so you want to convert everything into tan2y\tan^2 y.
Original post by SeanFM
That is still dx/dy but you've changed sec into cos, which can work but you don't need to do it.

Remember that dx/dy = 1/(dy/dx).

As Zacken is helping as well I will bow out. :hat2:


ohhh I see, thanks! :smile:


Posted from TSR Mobile
Original post by Zacken
No. You know that tan2y=x\tan^2 y = x and you want an answer involving xx so you want to convert everything into tan2y\tan^2 y.


got it, thanks!


Posted from TSR Mobile
Reply 17
Original post by bubblegumcat
got it, thanks!


Posted from TSR Mobile


Thank @SeanFM. :-)

Quick Reply