What is the derivative of ((5x-1)/(4x+2))^{-5} ?

The derivative of ((5x-1)/(4x+2))^{-5} is -(1120(2x+1)^4)/((5x-1)^6)

What is the first derivative of ((5x-1)/(4x+2))^{-5} ?

The first derivative of ((5x-1)/(4x+2))^{-5} is -(1120(2x+1)^4)/((5x-1)^6)

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derivative of

(\frac{5 x - 1}{4 x + 2})^{- 5}

- \frac{1120 ( 2 x + 1 ) ^{4}}{( 5 x - 1 ) ^{6}}

Solution steps

\frac{d}{d x} ((\frac{5 x - 1}{4 x + 2})^{- 5})

Apply the chain rule:

- \frac{5}{( \frac{5 x - 1}{4 x + 2} ) ^{6}} \frac{d}{d x} (\frac{5 x - 1}{4 x + 2})

= - \frac{5}{( \frac{5 x - 1}{4 x + 2} ) ^{6}} \frac{d}{d x} (\frac{5 x - 1}{4 x + 2})

\frac{d}{d x} (\frac{5 x - 1}{4 x + 2}) = \frac{7}{2 ( 2 x + 1 ) ^{2}}

= - \frac{5}{( \frac{5 x - 1}{4 x + 2} ) ^{6}} \cdot \frac{7}{2 ( 2 x + 1 ) ^{2}}

Simplify

- \frac{5}{( \frac{5 x - 1}{4 x + 2} ) ^{6}} \cdot \frac{7}{2 ( 2 x + 1 ) ^{2}} : - \frac{1120 ( 2 x + 1 ) ^{4}}{( 5 x - 1 ) ^{6}}

= - \frac{1120 ( 2 x + 1 ) ^{4}}{( 5 x - 1 ) ^{6}}

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What is the derivative of ((5x-1)/(4x+2))^{-5} ?
The derivative of ((5x-1)/(4x+2))^{-5} is -(1120(2x+1)^4)/((5x-1)^6)
What is the first derivative of ((5x-1)/(4x+2))^{-5} ?
The first derivative of ((5x-1)/(4x+2))^{-5} is -(1120(2x+1)^4)/((5x-1)^6)