What is the derivative of ((x^2+1)/(x^2-1))^5 ?

The derivative of ((x^2+1)/(x^2-1))^5 is -(20x(x^2+1)^4)/((x^2-1)^6)

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

The first derivative of ((x^2+1)/(x^2-1))^5 is -(20x(x^2+1)^4)/((x^2-1)^6)

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derivative of

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

- \frac{20 x ( x ^{2} + 1 ) ^{4}}{( x ^{2} - 1 ) ^{6}}

Solution steps

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

Apply the chain rule:

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

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

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

Simplify

5 (\frac{x ^{2} + 1}{x ^{2} - 1})^{4} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}}) : - \frac{20 x ( x ^{2} + 1 ) ^{4}}{( x ^{2} - 1 ) ^{6}}

= - \frac{20 x ( x ^{2} + 1 ) ^{4}}{( x ^{2} - 1 ) ^{6}}

\int \frac{3 \cdot 2 ^{x} - 2 \cdot 3 ^{x}}{2 x} d x

\frac{1}{x}

f (x) = 2 x^{2} - x

x d x + sin^{2} (\frac{y}{x}) (y d x - x d y) = 0

\int (r^{3} + 1)^{2} \cdot r^{2} d r

What is the derivative of ((x^2+1)/(x^2-1))^5 ?
The derivative of ((x^2+1)/(x^2-1))^5 is -(20x(x^2+1)^4)/((x^2-1)^6)
What is the first derivative of ((x^2+1)/(x^2-1))^5 ?
The first derivative of ((x^2+1)/(x^2-1))^5 is -(20x(x^2+1)^4)/((x^2-1)^6)