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How do you find the derivative of #y= (x) / ((1- x^2) ^ (-1/2))#?

Answer 1

Paisley Johnson

the answer #y'=[2x-4x^3]/[2sqrt[x^2-x^4]]#

#y= (x) / ((1- x^2) ^ (-1/2))#

we can rewrite it

#y=x*(1-x^2)^(1/2)=x*sqrt(1-x^2)#

#y=sqrt[x^2(1-x^2)]=sqrt[x^2-x^4]#

now derivate it

#y'=[2x-4x^3]/[2sqrt[x^2-x^4]]#

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Answer 2

Ezekiel Alexander

To find the derivative of ( y = \frac{x}{(1 - x^2)^{-1/2}} ), use the quotient rule and chain rule. The derivative is:

[ y' = \frac{(1 - x^2)^{-1/2} - x \cdot \frac{-1}{2}(1 - x^2)^{-3/2} \cdot (-2x)}{(1 - x^2)} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.