What is the derivative of y=((x^2+2)/(x^2-2))^8 ?

The derivative of y=((x^2+2)/(x^2-2))^8 is -(64x(x^2+2)^7)/((x^2-2)^9)

What is the first derivative of y=((x^2+2)/(x^2-2))^8 ?

The first derivative of y=((x^2+2)/(x^2-2))^8 is -(64x(x^2+2)^7)/((x^2-2)^9)

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derivative of

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

- \frac{64 x ( x ^{2} + 2 ) ^{7}}{( x ^{2} - 2 ) ^{9}}

Solution steps

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

Apply the chain rule:

8 (\frac{x ^{2} + 2}{x ^{2} - 2})^{7} \frac{d}{d x} (\frac{x ^{2} + 2}{x ^{2} - 2})

= 8 (\frac{x ^{2} + 2}{x ^{2} - 2})^{7} \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}}

= 8 (\frac{x ^{2} + 2}{x ^{2} - 2})^{7} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}})

Simplify

8 (\frac{x ^{2} + 2}{x ^{2} - 2})^{7} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}}) : - \frac{64 x ( x ^{2} + 2 ) ^{7}}{( x ^{2} - 2 ) ^{9}}

= - \frac{64 x ( x ^{2} + 2 ) ^{7}}{( x ^{2} - 2 ) ^{9}}

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What is the derivative of y=((x^2+2)/(x^2-2))^8 ?
The derivative of y=((x^2+2)/(x^2-2))^8 is -(64x(x^2+2)^7)/((x^2-2)^9)
What is the first derivative of y=((x^2+2)/(x^2-2))^8 ?
The first derivative of y=((x^2+2)/(x^2-2))^8 is -(64x(x^2+2)^7)/((x^2-2)^9)