What is the derivative of ((x^2+4)/(x^2-4))^2 ?

The derivative of ((x^2+4)/(x^2-4))^2 is -(32x(x^2+4))/((x^2-4)^3)

What is the first derivative of ((x^2+4)/(x^2-4))^2 ?

The first derivative of ((x^2+4)/(x^2-4))^2 is -(32x(x^2+4))/((x^2-4)^3)

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derivative of

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

- \frac{32 x ( x ^{2} + 4 )}{( x ^{2} - 4 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

= 2 \cdot \frac{x ^{2} + 4}{x ^{2} - 4} \frac{d}{d x} (\frac{x ^{2} + 4}{x ^{2} - 4})

\frac{d}{d x} (\frac{x ^{2} + 4}{x ^{2} - 4}) = - \frac{16 x}{( x ^{2} - 4 ) ^{2}}

= 2 \cdot \frac{x ^{2} + 4}{x ^{2} - 4} (- \frac{16 x}{( x ^{2} - 4 ) ^{2}})

Simplify

2 \cdot \frac{x ^{2} + 4}{x ^{2} - 4} (- \frac{16 x}{( x ^{2} - 4 ) ^{2}}) : - \frac{32 x ( x ^{2} + 4 )}{( x ^{2} - 4 ) ^{3}}

= - \frac{32 x ( x ^{2} + 4 )}{( x ^{2} - 4 ) ^{3}}

What is the derivative of ((x^2+4)/(x^2-4))^2 ?
The derivative of ((x^2+4)/(x^2-4))^2 is -(32x(x^2+4))/((x^2-4)^3)
What is the first derivative of ((x^2+4)/(x^2-4))^2 ?
The first derivative of ((x^2+4)/(x^2-4))^2 is -(32x(x^2+4))/((x^2-4)^3)