What is the derivative of ln((4x+1)/(2x-7)) ?

The derivative of ln((4x+1)/(2x-7)) is -(30)/((4x+1)(2x-7))

What is the first derivative of ln((4x+1)/(2x-7)) ?

The first derivative of ln((4x+1)/(2x-7)) is -(30)/((4x+1)(2x-7))

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derivative of

ln (\frac{4 x + 1}{2 x - 7})

- \frac{30}{( 4 x + 1 ) ( 2 x - 7 )}

Solution steps

\frac{d}{d x} (ln (\frac{4 x + 1}{2 x - 7}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{4 x + 1}{2 x - 7}) = - \frac{30}{( 2 x - 7 ) ^{2}}

= \frac{1}{\frac{4 x + 1}{2 x - 7}} (- \frac{30}{( 2 x - 7 ) ^{2}})

Simplify

\frac{1}{\frac{4 x + 1}{2 x - 7}} (- \frac{30}{( 2 x - 7 ) ^{2}}) : - \frac{30}{( 4 x + 1 ) ( 2 x - 7 )}

= - \frac{30}{( 4 x + 1 ) ( 2 x - 7 )}

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What is the derivative of ln((4x+1)/(2x-7)) ?
The derivative of ln((4x+1)/(2x-7)) is -(30)/((4x+1)(2x-7))
What is the first derivative of ln((4x+1)/(2x-7)) ?
The first derivative of ln((4x+1)/(2x-7)) is -(30)/((4x+1)(2x-7))