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

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

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

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

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

\frac{x}{1 - x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{x}{1 - x ^{2}}

\frac{1}{1 + s ^{2}}

\int 8 t^{3} - 6 t^{- 2} d t

x \to 5 + lim (\frac{2}{x - 5})

\int (e^{x} - 1)^{3} d x

f (x) = sin (5 x^{2})

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