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

The derivative of ((x^2+2/(x^2-2))^3) is -(24x(x^2+2)^2)/((x^2-2)^4)

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

The first derivative of ((x^2+2/(x^2-2))^3) is -(24x(x^2+2)^2)/((x^2-2)^4)

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

- \frac{24 x ( x ^{2} + 2 ) ^{2}}{( x ^{2} - 2 ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x ^{2} + 2}{x ^{2} - 2}) = - \frac{8 x}{( x ^{2} - 2 ) ^{2}}

= 3 (\frac{x ^{2} + 2}{x ^{2} - 2})^{2} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}})

Simplify

3 (\frac{x ^{2} + 2}{x ^{2} - 2})^{2} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}}) : - \frac{24 x ( x ^{2} + 2 ) ^{2}}{( x ^{2} - 2 ) ^{4}}

= - \frac{24 x ( x ^{2} + 2 ) ^{2}}{( x ^{2} - 2 ) ^{4}}

\frac{\partial}{\partial x} (x arctan (x + 2 y))

\frac{d}{d x} (\frac{2 cos ( x )}{x + 1})

\int \frac{( x - 2 )}{2} d x

\frac{d}{d x} (\frac{10 x}{x ^{2} - 6})

f (x) = x^{2} - 5, (- 3, 4)

What is the derivative of ((x^2+2/(x^2-2))^3) ?
The derivative of ((x^2+2/(x^2-2))^3) is -(24x(x^2+2)^2)/((x^2-2)^4)
What is the first derivative of ((x^2+2/(x^2-2))^3) ?
The first derivative of ((x^2+2/(x^2-2))^3) is -(24x(x^2+2)^2)/((x^2-2)^4)