Finding derivatives

1. Sep 27, 2009

sobek

How would I find the derivative of (1-x^2)^-1/4?
y = 1 + x - x^2 - x^4

I found the derivative to be 1 - 2x - 4x^3, but I need help solving it for 0. Thanks for your time.

2. Sep 27, 2009

HallsofIvy

Staff Emeritus
??? Are you talking about two different functions to differentiate? Yes, the derivative of y= 1+ x- x^2- x^4 is 1- 2x- 4x^3. There is a "cubic formula" but it is very complicated. If 1- 2x- 4x^3 does not have rational roots, there is not going to be any simple solution. If there are rational roots then they must be $\pm 1$, $\pm 1/2$, or $\pm 1/4$. Do any of those satisfy this equation? If so you can divide by x- that number to reduce the rest to a quadratic.

To differentiate (1- x^2)^(-1/4), use the chain rule. The derivative of ( )^(-1/4) is (-1/4)( )^(-1/4-1)= (-1/4( )^(-5/4) times the derivative of what ever is in the ( ). Here, that is 1- x^2 which has derivative -2x. The derivative of (1- x^2)^(-1/4) is (-1/4)(1- x^2)^(-5/4)(-2x)= (1/2)x(1- x^2)^(-5/4).