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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (7 cos (x) sin (y))

\frac{d}{d x} (\frac{e ^{3 x}}{x})

\frac{d}{d x} (ln (8 - 4 x))

\frac{d}{d x} (cos (x + e^{x}))

\frac{d}{d x} (\frac{x ^{2} + 4}{5 x - 9})

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