What is the (1/(sqrt(1-x^2)))^' ?

The (1/(sqrt(1-x^2)))^' is x/((1-x^2)^{3/2)}

What is the first (1/(sqrt(1-x^2)))^' ?

The first (1/(sqrt(1-x^2)))^' is x/((1-x^2)^{3/2)}

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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