1. The problem statement, all variables and given/known data 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] 2. Relevant 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. 3. 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.