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

The derivative of ((x^2+5)/(x^2-5))^2 is -(40x(x^2+5))/((x^2-5)^3)

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

The first derivative of ((x^2+5)/(x^2-5))^2 is -(40x(x^2+5))/((x^2-5)^3)

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derivative of

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

- \frac{40 x ( x ^{2} + 5 )}{( x ^{2} - 5 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x ^{2} + 5}{x ^{2} - 5}) = - \frac{20 x}{( x ^{2} - 5 ) ^{2}}

= 2 \cdot \frac{x ^{2} + 5}{x ^{2} - 5} (- \frac{20 x}{( x ^{2} - 5 ) ^{2}})

Simplify

2 \cdot \frac{x ^{2} + 5}{x ^{2} - 5} (- \frac{20 x}{( x ^{2} - 5 ) ^{2}}) : - \frac{40 x ( x ^{2} + 5 )}{( x ^{2} - 5 ) ^{3}}

= - \frac{40 x ( x ^{2} + 5 )}{( x ^{2} - 5 ) ^{3}}

\int sin (0)

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\frac{d}{d x} (2 x tan (x) + x^{2} sec^{2} (x))

\frac{d}{d x} (cos (π x^{2}))

n = 1 \sum \infty \frac{1}{4 n ^{2} - 1}

What is the derivative of ((x^2+5)/(x^2-5))^2 ?
The derivative of ((x^2+5)/(x^2-5))^2 is -(40x(x^2+5))/((x^2-5)^3)
What is the first derivative of ((x^2+5)/(x^2-5))^2 ?
The first derivative of ((x^2+5)/(x^2-5))^2 is -(40x(x^2+5))/((x^2-5)^3)