What is the derivative of ((x^2+1/(x^2-1))^6) ?

The derivative of ((x^2+1/(x^2-1))^6) is -(24x(x^2+1)^5)/((x^2-1)^7)

What is the first derivative of ((x^2+1/(x^2-1))^6) ?

The first derivative of ((x^2+1/(x^2-1))^6) is -(24x(x^2+1)^5)/((x^2-1)^7)

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

- \frac{24 x ( x ^{2} + 1 ) ^{5}}{( x ^{2} - 1 ) ^{7}}

Solution steps

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

Apply the chain rule:

6 (\frac{x ^{2} + 1}{x ^{2} - 1})^{5} \frac{d}{d x} (\frac{x ^{2} + 1}{x ^{2} - 1})

= 6 (\frac{x ^{2} + 1}{x ^{2} - 1})^{5} \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}}

= 6 (\frac{x ^{2} + 1}{x ^{2} - 1})^{5} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}})

Simplify

6 (\frac{x ^{2} + 1}{x ^{2} - 1})^{5} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}}) : - \frac{24 x ( x ^{2} + 1 ) ^{5}}{( x ^{2} - 1 ) ^{7}}

= - \frac{24 x ( x ^{2} + 1 ) ^{5}}{( x ^{2} - 1 ) ^{7}}

x \to 3 - lim (x^{2})

\int_{0}^{1} \frac{x ^{3} + 4}{x ^{2} - 25} d x

y = \frac{9 x}{x}

\int t \cdot cos (n t) d t

x + y

What is the derivative of ((x^2+1/(x^2-1))^6) ?
The derivative of ((x^2+1/(x^2-1))^6) is -(24x(x^2+1)^5)/((x^2-1)^7)
What is the first derivative of ((x^2+1/(x^2-1))^6) ?
The first derivative of ((x^2+1/(x^2-1))^6) is -(24x(x^2+1)^5)/((x^2-1)^7)