What is the derivative of ln(((4-3x^3)/(4x-3))) ?

The derivative of ln(((4-3x^3)/(4x-3))) is -(24x-11)/((-3x+4)(4x-3))

What is the first derivative of ln(((4-3x^3)/(4x-3))) ?

The first derivative of ln(((4-3x^3)/(4x-3))) is -(24x-11)/((-3x+4)(4x-3))

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

- \frac{24 x - 11}{( - 3 x + 4 ) ( 4 x - 3 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{( 4 - 3 x ) ^{3}}{4 x - 3}) = \frac{- 9 ( 4 - 3 x ) ^{2} ( 4 x - 3 ) - 4 ( 4 - 3 x ) ^{3}}{( 4 x - 3 ) ^{2}}

= \frac{1}{\frac{( 4 - 3 x ) ^{3}}{4 x - 3}} \cdot \frac{- 9 ( 4 - 3 x ) ^{2} ( 4 x - 3 ) - 4 ( 4 - 3 x ) ^{3}}{( 4 x - 3 ) ^{2}}

Simplify

\frac{1}{\frac{( 4 - 3 x ) ^{3}}{4 x - 3}} \cdot \frac{- 9 ( 4 - 3 x ) ^{2} ( 4 x - 3 ) - 4 ( 4 - 3 x ) ^{3}}{( 4 x - 3 ) ^{2}} : - \frac{24 x - 11}{( - 3 x + 4 ) ( 4 x - 3 )}

= - \frac{24 x - 11}{( - 3 x + 4 ) ( 4 x - 3 )}

\frac{d}{d x} ((1 - 2 x) e^{- x})

\frac{\partial}{\partial x} (x ln (y cos (x)))

\frac{d}{d x} (x^{4} - 10 x^{2} + 9)

\frac{d}{d x} (e^{x - 2 y})

\int \frac{x + 20}{x ^{2} + 18 x + 85} d x

What is the derivative of ln(((4-3x^3)/(4x-3))) ?
The derivative of ln(((4-3x^3)/(4x-3))) is -(24x-11)/((-3x+4)(4x-3))
What is the first derivative of ln(((4-3x^3)/(4x-3))) ?
The first derivative of ln(((4-3x^3)/(4x-3))) is -(24x-11)/((-3x+4)(4x-3))