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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{2} - 1) = 6 x

= - \frac{1}{2 ( 3 x ^{2} - 1 ) ^{\frac{3}{2}}} \cdot 6 x

Simplify

- \frac{1}{2 ( 3 x ^{2} - 1 ) ^{\frac{3}{2}}} \cdot 6 x : - \frac{3 x}{( 3 x ^{2} - 1 ) ^{\frac{3}{2}}}

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

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