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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (1 + \frac{1}{x})

\frac{10}{s ^{2}} - 1

f (x) = (2 x^{2} + 4 x)^{3}

x y^{^{'}} = y + 8 x^{2} sin (x), y (π) = 0

3 x^{2} + 4 x y + (2 y + 2 x^{2}) \frac{d y}{d x} = 0

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