What is the derivative of ln((5x+2/(5x-2))) ?

The derivative of ln((5x+2/(5x-2))) is -(20)/((5x+2)(5x-2))

What is the first derivative of ln((5x+2/(5x-2))) ?

The first derivative of ln((5x+2/(5x-2))) is -(20)/((5x+2)(5x-2))

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\frac{d}{d x} (ln (\frac{5 x + 2}{5 x - 2}))

- \frac{20}{( 5 x + 2 ) ( 5 x - 2 )}

Solution steps

\frac{d}{d x} (ln (\frac{5 x + 2}{5 x - 2}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{5 x + 2}{5 x - 2}) = - \frac{20}{( 5 x - 2 ) ^{2}}

= \frac{1}{\frac{5 x + 2}{5 x - 2}} (- \frac{20}{( 5 x - 2 ) ^{2}})

Simplify

\frac{1}{\frac{5 x + 2}{5 x - 2}} (- \frac{20}{( 5 x - 2 ) ^{2}}) : - \frac{20}{( 5 x + 2 ) ( 5 x - 2 )}

= - \frac{20}{( 5 x + 2 ) ( 5 x - 2 )}

f (x) = \frac{1}{3 x + 1}

y^{^{'}} = t e^{- y}, y (0) = 1

\int_{0}^{1} cos (2 π x) d x

x \to 3 lim (x - 1)

y^{^{''}} + 36 y = - 48 sin (6 t)

What is the derivative of ln((5x+2/(5x-2))) ?
The derivative of ln((5x+2/(5x-2))) is -(20)/((5x+2)(5x-2))
What is the first derivative of ln((5x+2/(5x-2))) ?
The first derivative of ln((5x+2/(5x-2))) is -(20)/((5x+2)(5x-2))