What is the derivative of ((x+3/(x-3))^5) ?

The derivative of ((x+3/(x-3))^5) is -(30(x+3)^4)/((x-3)^6)

What is the first derivative of ((x+3/(x-3))^5) ?

The first derivative of ((x+3/(x-3))^5) is -(30(x+3)^4)/((x-3)^6)

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\frac{d}{d x} ((\frac{x + 3}{x - 3})^{5})

- \frac{30 ( x + 3 ) ^{4}}{( x - 3 ) ^{6}}

Solution steps

\frac{d}{d x} ((\frac{x + 3}{x - 3})^{5})

Apply the chain rule:

5 (\frac{x + 3}{x - 3})^{4} \frac{d}{d x} (\frac{x + 3}{x - 3})

= 5 (\frac{x + 3}{x - 3})^{4} \frac{d}{d x} (\frac{x + 3}{x - 3})

\frac{d}{d x} (\frac{x + 3}{x - 3}) = - \frac{6}{( x - 3 ) ^{2}}

= 5 (\frac{x + 3}{x - 3})^{4} (- \frac{6}{( x - 3 ) ^{2}})

Simplify

5 (\frac{x + 3}{x - 3})^{4} (- \frac{6}{( x - 3 ) ^{2}}) : - \frac{30 ( x + 3 ) ^{4}}{( x - 3 ) ^{6}}

= - \frac{30 ( x + 3 ) ^{4}}{( x - 3 ) ^{6}}

What is the derivative of ((x+3/(x-3))^5) ?
The derivative of ((x+3/(x-3))^5) is -(30(x+3)^4)/((x-3)^6)
What is the first derivative of ((x+3/(x-3))^5) ?
The first derivative of ((x+3/(x-3))^5) is -(30(x+3)^4)/((x-3)^6)