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

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

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

The first derivative of sqrt(1/(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 the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (x^{2} + y^{2} + 2 x y)

\int 7 e^{- 0.8 x} d x

x \to \infty lim (x \frac{1}{2})

x \to 0 lim (x^{2} csc^{2} (\frac{x}{2}))

(- 9, 6), (- 6, - 9)

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