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

The derivative of y=((x^2+2)/(x^2-2))^6 is -(48x(x^2+2)^5)/((x^2-2)^7)

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

The first derivative of y=((x^2+2)/(x^2-2))^6 is -(48x(x^2+2)^5)/((x^2-2)^7)

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derivative of

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

- \frac{48 x ( x ^{2} + 2 ) ^{5}}{( x ^{2} - 2 ) ^{7}}

Solution steps

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

Apply the chain rule:

6 (\frac{x ^{2} + 2}{x ^{2} - 2})^{5} \frac{d}{d x} (\frac{x ^{2} + 2}{x ^{2} - 2})

= 6 (\frac{x ^{2} + 2}{x ^{2} - 2})^{5} \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}}

= 6 (\frac{x ^{2} + 2}{x ^{2} - 2})^{5} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}})

Simplify

6 (\frac{x ^{2} + 2}{x ^{2} - 2})^{5} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}}) : - \frac{48 x ( x ^{2} + 2 ) ^{5}}{( x ^{2} - 2 ) ^{7}}

= - \frac{48 x ( x ^{2} + 2 ) ^{5}}{( x ^{2} - 2 ) ^{7}}

\frac{\partial}{\partial x} (x ln (z^{3} + x^{6}))

y = tan (π - \frac{9}{x})

12 + 2.8 sin (\frac{2 π}{365} (t - 80))

n = 0 \sum \infty \frac{4}{2 ^{n}}

f (x) = cos (x)

What is the derivative of y=((x^2+2)/(x^2-2))^6 ?
The derivative of y=((x^2+2)/(x^2-2))^6 is -(48x(x^2+2)^5)/((x^2-2)^7)
What is the first derivative of y=((x^2+2)/(x^2-2))^6 ?
The first derivative of y=((x^2+2)/(x^2-2))^6 is -(48x(x^2+2)^5)/((x^2-2)^7)