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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derivative of

(\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} - 3 x) (2 x^{2} + 3 x + 5))

n = 0 \sum \infty \frac{1}{3 ^{n}}

\int \frac{15}{25 + x ^{2}} d x

x \to - 2 lim (\frac{2}{x + 2})

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)