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

Answer 1

Emilia Aguilar

Derivative of #color(blue)(d/dx(1/(1-x^2)^(1/2))=x/(1-x^2)^(3/2))#

Start with the given #1/(1-x^2)^(1/2)#

#d/dx(1/(1-x^2)^(1/2))=d/dx(1-x^2)^(-1/2)#

#d/dx(1/(1-x^2)^(1/2))=(-1/2)(1-x^2)^(-1/2-1)*d/dx(1-x^2)#

#d/dx(1/(1-x^2)^(1/2))=(-1/2)(1-x^2)^(-3/2)*(0-2x)#

#d/dx(1/(1-x^2)^(1/2))=(-1/2)(1-x^2)^(-3/2)*(-2x)#

#d/dx(1/(1-x^2)^(1/2))=x/(1-x^2)^(3/2)#

God bless....I hope the explanation is useful.

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Answer 2

Ezra Adams

To find the derivative of ( \frac{1}{(1-x^2)^{1/2}} ), you can use the chain rule and the power rule for differentiation. The derivative is:

[ \frac{d}{dx}\left(\frac{1}{(1-x^2)^{1/2}}\right) = \frac{d}{dx}\left((1-x^2)^{-1/2}\right) = \frac{-1}{2}(1-x^2)^{-3/2} \cdot \frac{d}{dx}(1-x^2) = \frac{x}{(1-x^2)^{3/2}} ]

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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.