What is the derivative of sqrt(1/(x^2-9)) ?

The derivative of sqrt(1/(x^2-9)) is -x/((x^2-9)^{3/2)}

What is the first derivative of sqrt(1/(x^2-9)) ?

The first derivative of sqrt(1/(x^2-9)) is -x/((x^2-9)^{3/2)}

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\frac{d}{d x} (\frac{1}{x ^{2} - 9})

- \frac{x}{( x ^{2} - 9 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{2} - 9})

Apply the chain rule:

\frac{1}{2 \frac{1}{x ^{2} - 9}} \frac{d}{d x} (\frac{1}{x ^{2} - 9})

= \frac{1}{2 \frac{1}{x ^{2} - 9}} \frac{d}{d x} (\frac{1}{x ^{2} - 9})

\frac{d}{d x} (\frac{1}{x ^{2} - 9}) = - \frac{2 x}{( x ^{2} - 9 ) ^{2}}

= \frac{1}{2 \frac{1}{x ^{2} - 9}} (- \frac{2 x}{( x ^{2} - 9 ) ^{2}})

Simplify

\frac{1}{2 \frac{1}{x ^{2} - 9}} (- \frac{2 x}{( x ^{2} - 9 ) ^{2}}) : - \frac{x}{( x ^{2} - 9 ) ^{\frac{3}{2}}}

= - \frac{x}{( x ^{2} - 9 ) ^{\frac{3}{2}}}

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

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

\frac{5 ( 1 - sin ( x ) )}{2 cos ( x )}

x^{^{'}} = x^{3} (t)

x^{3} + 2 x + 1

What is the derivative of sqrt(1/(x^2-9)) ?
The derivative of sqrt(1/(x^2-9)) is -x/((x^2-9)^{3/2)}
What is the first derivative of sqrt(1/(x^2-9)) ?
The first derivative of sqrt(1/(x^2-9)) is -x/((x^2-9)^{3/2)}