What is the derivative of ((x+9)/(x-9))^5 ?

The derivative of ((x+9)/(x-9))^5 is -(90(x+9)^4)/((x-9)^6)

What is the first derivative of ((x+9)/(x-9))^5 ?

The first derivative of ((x+9)/(x-9))^5 is -(90(x+9)^4)/((x-9)^6)

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derivative of

(\frac{x + 9}{x - 9})^{5}

- \frac{90 ( x + 9 ) ^{4}}{( x - 9 ) ^{6}}

Solution steps

\frac{d}{d x} ((\frac{x + 9}{x - 9})^{5})

Apply the chain rule:

5 (\frac{x + 9}{x - 9})^{4} \frac{d}{d x} (\frac{x + 9}{x - 9})

= 5 (\frac{x + 9}{x - 9})^{4} \frac{d}{d x} (\frac{x + 9}{x - 9})

\frac{d}{d x} (\frac{x + 9}{x - 9}) = - \frac{18}{( x - 9 ) ^{2}}

= 5 (\frac{x + 9}{x - 9})^{4} (- \frac{18}{( x - 9 ) ^{2}})

Simplify

5 (\frac{x + 9}{x - 9})^{4} (- \frac{18}{( x - 9 ) ^{2}}) : - \frac{90 ( x + 9 ) ^{4}}{( x - 9 ) ^{6}}

= - \frac{90 ( x + 9 ) ^{4}}{( x - 9 ) ^{6}}

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What is the derivative of ((x+9)/(x-9))^5 ?
The derivative of ((x+9)/(x-9))^5 is -(90(x+9)^4)/((x-9)^6)
What is the first derivative of ((x+9)/(x-9))^5 ?
The first derivative of ((x+9)/(x-9))^5 is -(90(x+9)^4)/((x-9)^6)