What is the derivative of (1-x^2^{-1/2}) ?

The derivative of (1-x^2^{-1/2}) is x/((1-x^2)^{3/2)}

What is the first derivative of (1-x^2^{-1/2}) ?

The first derivative of (1-x^2^{-1/2}) is x/((1-x^2)^{3/2)}

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\frac{d}{d x} ((1 - x^{2})^{- \frac{1}{2}})

\frac{x}{( 1 - x ^{2} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} ((1 - x^{2})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 1 - x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (1 - x^{2})

= - \frac{1}{2 ( 1 - x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (1 - x^{2})

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

= - \frac{1}{2 ( 1 - x ^{2} ) ^{\frac{3}{2}}} (- 2 x)

Simplify

- \frac{1}{2 ( 1 - x ^{2} ) ^{\frac{3}{2}}} (- 2 x) : \frac{x}{( 1 - x ^{2} ) ^{\frac{3}{2}}}

= \frac{x}{( 1 - x ^{2} ) ^{\frac{3}{2}}}

What is the derivative of (1-x^2^{-1/2}) ?
The derivative of (1-x^2^{-1/2}) is x/((1-x^2)^{3/2)}
What is the first derivative of (1-x^2^{-1/2}) ?
The first derivative of (1-x^2^{-1/2}) is x/((1-x^2)^{3/2)}