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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

\int \frac{x}{x ^{2} - 9} d x

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

\frac{\partial}{\partial x} (2 x sin (x y))

x v^{'} + 2 v = 0

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