What is the derivative of ((x+4/(x-4))^5) ?

The derivative of ((x+4/(x-4))^5) is -(40(x+4)^4)/((x-4)^6)

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

The first derivative of ((x+4/(x-4))^5) is -(40(x+4)^4)/((x-4)^6)

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

- \frac{40 ( x + 4 ) ^{4}}{( x - 4 ) ^{6}}

Solution steps

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

Apply the chain rule:

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

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

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

= 5 (\frac{x + 4}{x - 4})^{4} (- \frac{8}{( x - 4 ) ^{2}})

Simplify

5 (\frac{x + 4}{x - 4})^{4} (- \frac{8}{( x - 4 ) ^{2}}) : - \frac{40 ( x + 4 ) ^{4}}{( x - 4 ) ^{6}}

= - \frac{40 ( x + 4 ) ^{4}}{( x - 4 ) ^{6}}

What is the derivative of ((x+4/(x-4))^5) ?
The derivative of ((x+4/(x-4))^5) is -(40(x+4)^4)/((x-4)^6)
What is the first derivative of ((x+4/(x-4))^5) ?
The first derivative of ((x+4/(x-4))^5) is -(40(x+4)^4)/((x-4)^6)