What is the derivative of ((2x-3^{-3})/((2-3x)^2)) ?

The derivative of ((2x-3^{-3})/((2-3x)^2)) is -(30(x-1))/((2x-3)^4(3x-2)^3)

What is the first derivative of ((2x-3^{-3})/((2-3x)^2)) ?

The first derivative of ((2x-3^{-3})/((2-3x)^2)) is -(30(x-1))/((2x-3)^4(3x-2)^3)

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

- \frac{30 ( x - 1 )}{( 2 x - 3 ) ^{4} ( 3 x - 2 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{( - \frac{6}{( 2 x - 3 ) ^{4}} ) ( 2 - 3 x ) ^{2} - ( - 6 ( 2 - 3 x ) ) ( 2 x - 3 ) ^{- 3}}{( ( 2 - 3 x ) ^{2} ) ^{2}} : - \frac{30 ( x - 1 )}{( 2 x - 3 ) ^{4} ( 3 x - 2 ) ^{3}}

= - \frac{30 ( x - 1 )}{( 2 x - 3 ) ^{4} ( 3 x - 2 ) ^{3}}

What is the derivative of ((2x-3^{-3})/((2-3x)^2)) ?
The derivative of ((2x-3^{-3})/((2-3x)^2)) is -(30(x-1))/((2x-3)^4(3x-2)^3)
What is the first derivative of ((2x-3^{-3})/((2-3x)^2)) ?
The first derivative of ((2x-3^{-3})/((2-3x)^2)) is -(30(x-1))/((2x-3)^4(3x-2)^3)