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

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

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

The first derivative of 1/(sqrt(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 exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 3 x e^{4 x} d x

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

s^{2} + t^{2}

\int e^{c o s (π x)} sin (π x) d x

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