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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derivative of

(\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}}

\int \frac{1}{2 - x ^{2}} d x

n = 4 \sum \infty \frac{8}{n ^{2} - 1}

2 x^{2}, 2 x + 6, - 1, 0

x y + 4 y = 10

x \to 2 lim (\frac{5 x ^{3}}{x + 3})

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)