What is the derivative of ((x^2+3/(x^2-3))^2) ?

The derivative of ((x^2+3/(x^2-3))^2) is -(24x(x^2+3))/((x^2-3)^3)

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

The first derivative of ((x^2+3/(x^2-3))^2) is -(24x(x^2+3))/((x^2-3)^3)

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

- \frac{24 x ( x ^{2} + 3 )}{( x ^{2} - 3 ) ^{3}}

Solution steps

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

Apply the chain rule:

2 \cdot \frac{x ^{2} + 3}{x ^{2} - 3} \frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3})

= 2 \cdot \frac{x ^{2} + 3}{x ^{2} - 3} \frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3})

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3}) = - \frac{12 x}{( x ^{2} - 3 ) ^{2}}

= 2 \cdot \frac{x ^{2} + 3}{x ^{2} - 3} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}})

Simplify

2 \cdot \frac{x ^{2} + 3}{x ^{2} - 3} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}}) : - \frac{24 x ( x ^{2} + 3 )}{( x ^{2} - 3 ) ^{3}}

= - \frac{24 x ( x ^{2} + 3 )}{( x ^{2} - 3 ) ^{3}}

What is the derivative of ((x^2+3/(x^2-3))^2) ?
The derivative of ((x^2+3/(x^2-3))^2) is -(24x(x^2+3))/((x^2-3)^3)
What is the first derivative of ((x^2+3/(x^2-3))^2) ?
The first derivative of ((x^2+3/(x^2-3))^2) is -(24x(x^2+3))/((x^2-3)^3)