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Hi all...not sure if this should be here, perhaps in the precalc section =S but here goes anyways...

1. So the question asks to find the derivative of y = sqrt(arctan x), then to simplify wherever possible...my issue is not with the differentiation, but rather with the simplifying...oh and we also need to use implicit differentiation when doing so, see my attempt at the solution below.

3. I basically manipulated the eqn so it was x = tan (sqrt (y)), and then found dy/dx by implicitly differentiating...then i eventually got to this:

dy/dx = (2sqrt (y))/(sec^2 (sqrt(y)))

AND we have y explicitly, so we can substitute y = sqrt(arctan)...so I do that, and I get...

dy/dx = (2sqrt (sqrt(arctan)))/(sec^2 (sqrt(sqrt(arctan))))

which is the same as

dy/dx = (2qrrt(arctan))/(sec^2 (qrrt(arctan))) (qrrt = quartic root of...i'm not sure if that's legit or not...)

so my final answer was dy/dx = (2qrrt(arctan))/(sec^2 (qrrt(arctan))) but the question says simplify, and after an hour of staring at this, i can't seem to figure out what more to simplify?!

Am i missing something? Can i simplify further in this case?

Thanks so much for your help in advance!

1. So the question asks to find the derivative of y = sqrt(arctan x), then to simplify wherever possible...my issue is not with the differentiation, but rather with the simplifying...oh and we also need to use implicit differentiation when doing so, see my attempt at the solution below.

**2. No relevant formulae**3. I basically manipulated the eqn so it was x = tan (sqrt (y)), and then found dy/dx by implicitly differentiating...then i eventually got to this:

dy/dx = (2sqrt (y))/(sec^2 (sqrt(y)))

AND we have y explicitly, so we can substitute y = sqrt(arctan)...so I do that, and I get...

dy/dx = (2sqrt (sqrt(arctan)))/(sec^2 (sqrt(sqrt(arctan))))

which is the same as

dy/dx = (2qrrt(arctan))/(sec^2 (qrrt(arctan))) (qrrt = quartic root of...i'm not sure if that's legit or not...)

so my final answer was dy/dx = (2qrrt(arctan))/(sec^2 (qrrt(arctan))) but the question says simplify, and after an hour of staring at this, i can't seem to figure out what more to simplify?!

Am i missing something? Can i simplify further in this case?

Thanks so much for your help in advance!

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