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

The derivative of ((3x+3/(x-5))^5) is -(90(3x+3)^4)/((x-5)^6)

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

The first derivative of ((3x+3/(x-5))^5) is -(90(3x+3)^4)/((x-5)^6)

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

- \frac{90 ( 3 x + 3 ) ^{4}}{( x - 5 ) ^{6}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{3 x + 3}{x - 5}) = - \frac{18}{( x - 5 ) ^{2}}

= 5 (\frac{3 x + 3}{x - 5})^{4} (- \frac{18}{( x - 5 ) ^{2}})

Simplify

5 (\frac{3 x + 3}{x - 5})^{4} (- \frac{18}{( x - 5 ) ^{2}}) : - \frac{90 ( 3 x + 3 ) ^{4}}{( x - 5 ) ^{6}}

= - \frac{90 ( 3 x + 3 ) ^{4}}{( x - 5 ) ^{6}}

What is the derivative of ((3x+3/(x-5))^5) ?
The derivative of ((3x+3/(x-5))^5) is -(90(3x+3)^4)/((x-5)^6)
What is the first derivative of ((3x+3/(x-5))^5) ?
The first derivative of ((3x+3/(x-5))^5) is -(90(3x+3)^4)/((x-5)^6)