Derivative of y = x(1 - x²)^(1/2)

[Leonidas]

I keep on getting a weird answer when i take the dy/dx for this...
y=x(1-x^2)^1/2

i got x(1/x^2)^(-1/2)*-2x + (1-x^2)^(1/2)

... did i do that correctly?

 

[kreil]

$$y=x(1-x^2)^\frac{1}{2}$$

Use product rule/chain rule:

$$y=(x)(\frac{1}{2})(\frac{1}{\sqrt{1-x^2}})(-2x) + (1-x^2)^\frac{1}{2}$$

Slightly more simplified:

$$y=(\frac{-x^2}{\sqrt{1-x^2}}) + (1-x^2)^\frac{1}{2}$$

Pretty sure that's the answer...if so you aren't using the chain rule correctly. Double check how you get the derivative of $$(1-x^2)^\frac{1}{2}$$

 

[Leonidas]

DUH. *slaps self on forhead* ... heh... forgot a single step and it screwed me up (of course).

Thanks.