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

The derivative of ((x^2+3)/(x^2-3))^3 is -(36x(x^2+3)^2)/((x^2-3)^4)

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

The first derivative of ((x^2+3)/(x^2-3))^3 is -(36x(x^2+3)^2)/((x^2-3)^4)

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derivative of

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

- \frac{36 x ( x ^{2} + 3 ) ^{2}}{( x ^{2} - 3 ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

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

Simplify

3 (\frac{x ^{2} + 3}{x ^{2} - 3})^{2} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}}) : - \frac{36 x ( x ^{2} + 3 ) ^{2}}{( x ^{2} - 3 ) ^{4}}

= - \frac{36 x ( x ^{2} + 3 ) ^{2}}{( x ^{2} - 3 ) ^{4}}

What is the derivative of ((x^2+3)/(x^2-3))^3 ?
The derivative of ((x^2+3)/(x^2-3))^3 is -(36x(x^2+3)^2)/((x^2-3)^4)
What is the first derivative of ((x^2+3)/(x^2-3))^3 ?
The first derivative of ((x^2+3)/(x^2-3))^3 is -(36x(x^2+3)^2)/((x^2-3)^4)