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

The derivative of ((x^2+2/(x^2-2))^4) is -(32x(x^2+2)^3)/((x^2-2)^5)

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

The first derivative of ((x^2+2/(x^2-2))^4) is -(32x(x^2+2)^3)/((x^2-2)^5)

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

- \frac{32 x ( x ^{2} + 2 ) ^{3}}{( x ^{2} - 2 ) ^{5}}

Solution steps

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

Apply the chain rule:

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

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

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

Simplify

4 (\frac{x ^{2} + 2}{x ^{2} - 2})^{3} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}}) : - \frac{32 x ( x ^{2} + 2 ) ^{3}}{( x ^{2} - 2 ) ^{5}}

= - \frac{32 x ( x ^{2} + 2 ) ^{3}}{( x ^{2} - 2 ) ^{5}}

\int (sec (x))^{5} d x

\int (\frac{1}{x ^{5}} - x^{5} - \frac{1}{7}) d x

\frac{d}{d x} (\frac{1}{2} (e^{x} - cos (x)))

\frac{\partial}{\partial x} (\frac{y}{x} + x - y^{2})

\int 7 x e^{x} d x

What is the derivative of ((x^2+2/(x^2-2))^4) ?
The derivative of ((x^2+2/(x^2-2))^4) is -(32x(x^2+2)^3)/((x^2-2)^5)
What is the first derivative of ((x^2+2/(x^2-2))^4) ?
The first derivative of ((x^2+2/(x^2-2))^4) is -(32x(x^2+2)^3)/((x^2-2)^5)