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

The derivative of 1/(xsqrt(1-x^2)) is -(-2x^2+1)/(x^2(1-x^2)sqrt(1-x^2))

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

The first derivative of 1/(xsqrt(1-x^2)) is -(-2x^2+1)/(x^2(1-x^2)sqrt(1-x^2))

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (5 g (x) (2 x^{3}) + \frac{2}{x ^{2}})

y^{^{'}} - \frac{4}{x} y = x^{4} e^{x}

\int_{0}^{3} e^{- 2 x} d x

f (x) = \frac{sin ( x ^{2} )}{ln ( 2 x + 8 )}

\frac{d}{d n} (ln (n^{5} + 5 n))

What is the derivative of 1/(xsqrt(1-x^2)) ?
The derivative of 1/(xsqrt(1-x^2)) is -(-2x^2+1)/(x^2(1-x^2)sqrt(1-x^2))
What is the first derivative of 1/(xsqrt(1-x^2)) ?
The first derivative of 1/(xsqrt(1-x^2)) is -(-2x^2+1)/(x^2(1-x^2)sqrt(1-x^2))