What is the derivative of ln(1/(2x+3)) ?

The derivative of ln(1/(2x+3)) is -2/(2x+3)

What is the first derivative of ln(1/(2x+3)) ?

The first derivative of ln(1/(2x+3)) is -2/(2x+3)

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derivative of

ln (\frac{1}{2 x + 3})

- \frac{2}{2 x + 3}

Solution steps

\frac{d}{d x} (ln (\frac{1}{2 x + 3}))

Simplify

ln (\frac{1}{2 x + 3}) : - ln (2 x + 3)

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

\frac{1}{2 x + 3} \frac{d}{d x} (2 x + 3)

= \frac{1}{2 x + 3} \frac{d}{d x} (2 x + 3)

\frac{d}{d x} (2 x + 3) = 2

= - \frac{1}{2 x + 3} \cdot 2

Simplify

- \frac{1}{2 x + 3} \cdot 2 : - \frac{2}{2 x + 3}

= - \frac{2}{2 x + 3}

\frac{1}{( 5 \cdot s + 1 )}

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

\frac{d}{d x} (\frac{a x}{x ^{2} + a ^{2}})

\int (x^{4} + 2 x - 16) d x

\frac{d}{d x} (e^{x^{3}})

What is the derivative of ln(1/(2x+3)) ?
The derivative of ln(1/(2x+3)) is -2/(2x+3)
What is the first derivative of ln(1/(2x+3)) ?
The first derivative of ln(1/(2x+3)) is -2/(2x+3)