tan^-1(x/(1-x^2)^1/2) find the derivative
the problem comes from 3g from MIT's PDF I found
here is the solution key
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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