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

The derivative of ((x^2+1/(x^2-1))^3) is -(12x(x^2+1)^2)/((x^2-1)^4)

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

The first derivative of ((x^2+1/(x^2-1))^3) is -(12x(x^2+1)^2)/((x^2-1)^4)

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

- \frac{12 x ( x ^{2} + 1 ) ^{2}}{( x ^{2} - 1 ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

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

= 3 (\frac{x ^{2} + 1}{x ^{2} - 1})^{2} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}})

Simplify

3 (\frac{x ^{2} + 1}{x ^{2} - 1})^{2} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}}) : - \frac{12 x ( x ^{2} + 1 ) ^{2}}{( x ^{2} - 1 ) ^{4}}

= - \frac{12 x ( x ^{2} + 1 ) ^{2}}{( x ^{2} - 1 ) ^{4}}

What is the derivative of ((x^2+1/(x^2-1))^3) ?
The derivative of ((x^2+1/(x^2-1))^3) is -(12x(x^2+1)^2)/((x^2-1)^4)
What is the first derivative of ((x^2+1/(x^2-1))^3) ?
The first derivative of ((x^2+1/(x^2-1))^3) is -(12x(x^2+1)^2)/((x^2-1)^4)