quozzy
Oct21-09, 08:25 PM
Alright, I'm not technically stuck on this one, but I consistently get a result that disagrees with what Wolfram Alpha shows when I enter the problem to check my answer. Sorry 'bout the lack of LaTeX, but it should be simple enough to read. Here goes:
Problem:
Differentiate y=sin-1[x/(1+x)]
Basically, I rearrange for
sin(y)=x/(x+1)
then use implicit differentiation to yield:
* ---> cos(y)*(dy/(dx))=1/(x+1)2
Substituting with:
cos(y)=sqrt[1-sin2(y)]
I get:
cos(y)=sqrt[1-x2/(x+1)2]
which simplifies to:
cos(y)=sqrt(2x+1)/(x+1)
Dividing both sides of the original equation (above, marked with a star) by cos(y):
dy/(dx)=1/[(x+1)sqrt(2x+1)]
Which, if you don't like surds in the denominator, can be simplified to:
sqrt(2x+1)/[(x+1)(2x+1)]
I've done this question several times, and re-checked all my working. For the life of me, I can't see where I go wrong, yet my result is slightly different to what it should be. Any suggestions would be most welcome.
Problem:
Differentiate y=sin-1[x/(1+x)]
Basically, I rearrange for
sin(y)=x/(x+1)
then use implicit differentiation to yield:
* ---> cos(y)*(dy/(dx))=1/(x+1)2
Substituting with:
cos(y)=sqrt[1-sin2(y)]
I get:
cos(y)=sqrt[1-x2/(x+1)2]
which simplifies to:
cos(y)=sqrt(2x+1)/(x+1)
Dividing both sides of the original equation (above, marked with a star) by cos(y):
dy/(dx)=1/[(x+1)sqrt(2x+1)]
Which, if you don't like surds in the denominator, can be simplified to:
sqrt(2x+1)/[(x+1)(2x+1)]
I've done this question several times, and re-checked all my working. For the life of me, I can't see where I go wrong, yet my result is slightly different to what it should be. Any suggestions would be most welcome.