What is the derivative of ((x^2+1/(x^2-1))^7) ?

The derivative of ((x^2+1/(x^2-1))^7) is -(28x(x^2+1)^6)/((x^2-1)^8)

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

The first derivative of ((x^2+1/(x^2-1))^7) is -(28x(x^2+1)^6)/((x^2-1)^8)

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

- \frac{28 x ( x ^{2} + 1 ) ^{6}}{( x ^{2} - 1 ) ^{8}}

Solution steps

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

Apply the chain rule:

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

= 7 (\frac{x ^{2} + 1}{x ^{2} - 1})^{6} \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}}

= 7 (\frac{x ^{2} + 1}{x ^{2} - 1})^{6} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}})

Simplify

7 (\frac{x ^{2} + 1}{x ^{2} - 1})^{6} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}}) : - \frac{28 x ( x ^{2} + 1 ) ^{6}}{( x ^{2} - 1 ) ^{8}}

= - \frac{28 x ( x ^{2} + 1 ) ^{6}}{( x ^{2} - 1 ) ^{8}}

\frac{d}{d x} (x^{3} + 4)

\frac{6}{x ^{2} + 4}

\frac{\partial}{\partial x} (4 π^{2} \frac{y}{x ^{2}})

arctan (2 x)

x \to 0 lim (\frac{2 x}{0})

What is the derivative of ((x^2+1/(x^2-1))^7) ?
The derivative of ((x^2+1/(x^2-1))^7) is -(28x(x^2+1)^6)/((x^2-1)^8)
What is the first derivative of ((x^2+1/(x^2-1))^7) ?
The first derivative of ((x^2+1/(x^2-1))^7) is -(28x(x^2+1)^6)/((x^2-1)^8)