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## Homework Statement

tan^-1(x/(1-x^2)^1/2) find the derivative

the problem comes from 3g from MIT's PDF I found

http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-b-implicit-differentiation-and-inverse-functions/problem-set-2/MIT18_01SC_pset5sol.pdf [Broken]

here is the solution key

http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-b-implicit-differentiation-and-inverse-functions/problem-set-2/MIT18_01SC_pset5prb.pdf [Broken]

## Homework Equations

The solution key says if y = x/(1-x^2)^1/2 then y' = (1-x^2)^-3/2 When I do it, y' comes out differently. This is how I attempt to solve it.

## The Attempt at a Solution

Original problem: tan^-1((x/(1-x^2)^1/2)) what is the derivative with respect to x?

let y=x/(1-x^2)^1/2 y=x*(1-x^2)^-1/2 using the product rule I get:

y'=(1)(1-x^2)^-1/2 + x(-1/2)((1-x^2)^-3/2)(-2)

y'=(1-x^2)^-1/2 + (x^2)(1-x^2)^-3/2

This looks a lot different than the y' stated in the solution manual: y' = (1-x^2)^-3/2

Am I on the right track? Is the solution manual wrong? or am I missing a step? Thank you ahead.

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