What is the derivative of 1√1−x2?

2 Answers
Ada C.
Apr 12, 2018

=(x)(1−x2)−32

Explanation:

f(x)=1√1−x2=(√1−x2)−1=(1−x2)−12
ddxf(x)=−12(1−x2)−12−1(0−2x)
=2x2(1−x2)−32
=(x)(1−x2)−32

Aviv S.
Apr 12, 2018

The derivative is x√1−x2(1−x2)2.

Explanation:

Using the quotient rule:

=ddx[1√1−x2]

=ddx[1]⋅√1−x2−1⋅ddx[√1−x2](√1−x2)2

=0⋅√1−x2−1⋅ddx[√1−x2]1−x2

=−ddx[√1−x2]1−x2

Chain rule:

=−12√1−x2⋅ddx[1−x2]1−x2

=−12√1−x2⋅−2x1−x2

=x√1−x21−x2

=x√1−x21−x21−x2

=x√1−x2(1−x2)2

That's the derivative. Hope this helped!

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