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

The derivative of 2/((x^2-1)) is -(4x)/((x^2-1)^2)

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

The first derivative of 2/((x^2-1)) is -(4x)/((x^2-1)^2)

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derivative of

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

- \frac{4 x}{( x ^{2} - 1 ) ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

2 (- \frac{1}{( x ^{2} - 1 ) ^{2}} \cdot 2 x) : - \frac{4 x}{( x ^{2} - 1 ) ^{2}}

= - \frac{4 x}{( x ^{2} - 1 ) ^{2}}

What is the derivative of 2/((x^2-1)) ?
The derivative of 2/((x^2-1)) is -(4x)/((x^2-1)^2)
What is the first derivative of 2/((x^2-1)) ?
The first derivative of 2/((x^2-1)) is -(4x)/((x^2-1)^2)