What is the derivative of ((x^2+6/(x^2-6))^3) ?

The derivative of ((x^2+6/(x^2-6))^3) is -(72x(x^2+6)^2)/((x^2-6)^4)

What is the first derivative of ((x^2+6/(x^2-6))^3) ?

The first derivative of ((x^2+6/(x^2-6))^3) is -(72x(x^2+6)^2)/((x^2-6)^4)

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\frac{d}{d x} ((\frac{x ^{2} + 6}{x ^{2} - 6})^{3})

- \frac{72 x ( x ^{2} + 6 ) ^{2}}{( x ^{2} - 6 ) ^{4}}

Solution steps

\frac{d}{d x} ((\frac{x ^{2} + 6}{x ^{2} - 6})^{3})

Apply the chain rule:

3 (\frac{x ^{2} + 6}{x ^{2} - 6})^{2} \frac{d}{d x} (\frac{x ^{2} + 6}{x ^{2} - 6})

= 3 (\frac{x ^{2} + 6}{x ^{2} - 6})^{2} \frac{d}{d x} (\frac{x ^{2} + 6}{x ^{2} - 6})

\frac{d}{d x} (\frac{x ^{2} + 6}{x ^{2} - 6}) = - \frac{24 x}{( x ^{2} - 6 ) ^{2}}

= 3 (\frac{x ^{2} + 6}{x ^{2} - 6})^{2} (- \frac{24 x}{( x ^{2} - 6 ) ^{2}})

Simplify

3 (\frac{x ^{2} + 6}{x ^{2} - 6})^{2} (- \frac{24 x}{( x ^{2} - 6 ) ^{2}}) : - \frac{72 x ( x ^{2} + 6 ) ^{2}}{( x ^{2} - 6 ) ^{4}}

= - \frac{72 x ( x ^{2} + 6 ) ^{2}}{( x ^{2} - 6 ) ^{4}}

\frac{A}{y ^{7}} + B e^{y}

n = 1 \sum \infty \frac{3 - 2 n}{4 n}

(- 2, 7), (2, 3)

\int sin^{4} (a x) d x

\frac{d}{d x} (10 x e^{- 2 x})

What is the derivative of ((x^2+6/(x^2-6))^3) ?
The derivative of ((x^2+6/(x^2-6))^3) is -(72x(x^2+6)^2)/((x^2-6)^4)
What is the first derivative of ((x^2+6/(x^2-6))^3) ?
The first derivative of ((x^2+6/(x^2-6))^3) is -(72x(x^2+6)^2)/((x^2-6)^4)