- #1

- 15

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**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-sin

^{2}(y)]

I get:

cos(y)=sqrt[1-x

^{2}/(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.