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

The derivative of ((x^2+4/(x^2-4))^3) is -(48x(x^2+4)^2)/((x^2-4)^4)

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

The first derivative of ((x^2+4/(x^2-4))^3) is -(48x(x^2+4)^2)/((x^2-4)^4)

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

- \frac{48 x ( x ^{2} + 4 ) ^{2}}{( x ^{2} - 4 ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

= 3 (\frac{x ^{2} + 4}{x ^{2} - 4})^{2} (- \frac{16 x}{( x ^{2} - 4 ) ^{2}})

Simplify

3 (\frac{x ^{2} + 4}{x ^{2} - 4})^{2} (- \frac{16 x}{( x ^{2} - 4 ) ^{2}}) : - \frac{48 x ( x ^{2} + 4 ) ^{2}}{( x ^{2} - 4 ) ^{4}}

= - \frac{48 x ( x ^{2} + 4 ) ^{2}}{( x ^{2} - 4 ) ^{4}}

\int \frac{2 x + 3}{4 x ^{2} - 9} d x

x \to 0 lim (\frac{x + 2}{x ^{2}})

x \to - 4 lim (x^{2} + 3 x - 7)

\frac{\partial}{\partial y} (x z cos (x + yz))

\frac{d}{d x} (sin^{2} (ln (x)))

What is the derivative of ((x^2+4/(x^2-4))^3) ?
The derivative of ((x^2+4/(x^2-4))^3) is -(48x(x^2+4)^2)/((x^2-4)^4)
What is the first derivative of ((x^2+4/(x^2-4))^3) ?
The first derivative of ((x^2+4/(x^2-4))^3) is -(48x(x^2+4)^2)/((x^2-4)^4)