What is the derivative of ((3x+2/(x-1))^7) ?

The derivative of ((3x+2/(x-1))^7) is -(35(3x+2)^6)/((x-1)^8)

What is the first derivative of ((3x+2/(x-1))^7) ?

The first derivative of ((3x+2/(x-1))^7) is -(35(3x+2)^6)/((x-1)^8)

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\frac{d}{d x} ((\frac{3 x + 2}{x - 1})^{7})

- \frac{35 ( 3 x + 2 ) ^{6}}{( x - 1 ) ^{8}}

Solution steps

\frac{d}{d x} ((\frac{3 x + 2}{x - 1})^{7})

Apply the chain rule:

7 (\frac{3 x + 2}{x - 1})^{6} \frac{d}{d x} (\frac{3 x + 2}{x - 1})

= 7 (\frac{3 x + 2}{x - 1})^{6} \frac{d}{d x} (\frac{3 x + 2}{x - 1})

\frac{d}{d x} (\frac{3 x + 2}{x - 1}) = - \frac{5}{( x - 1 ) ^{2}}

= 7 (\frac{3 x + 2}{x - 1})^{6} (- \frac{5}{( x - 1 ) ^{2}})

Simplify

7 (\frac{3 x + 2}{x - 1})^{6} (- \frac{5}{( x - 1 ) ^{2}}) : - \frac{35 ( 3 x + 2 ) ^{6}}{( x - 1 ) ^{8}}

= - \frac{35 ( 3 x + 2 ) ^{6}}{( x - 1 ) ^{8}}

What is the derivative of ((3x+2/(x-1))^7) ?
The derivative of ((3x+2/(x-1))^7) is -(35(3x+2)^6)/((x-1)^8)
What is the first derivative of ((3x+2/(x-1))^7) ?
The first derivative of ((3x+2/(x-1))^7) is -(35(3x+2)^6)/((x-1)^8)