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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\frac{d}{d x} ((\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}}

x \to - 6 - lim (\frac{x + 2}{x + 6})

\int \frac{9}{x ^{2} - 9 x} d x

\frac{x}{1 + x ^{2}}

\int a x^{2} d x

5 - (x - 9)^{4}

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)