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

The derivative of (ln(x)/(2+ln(x))) is 2/(x(2+ln(x))^2)

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

The first derivative of (ln(x)/(2+ln(x))) is 2/(x(2+ln(x))^2)

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

\frac{2}{x ( 2 + ln ( x ) ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

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

Simplify

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

= \frac{2}{x ( 2 + ln ( x ) ) ^{2}}

x \to - 3 lim (2 x^{2})

\frac{d}{d x} (\frac{8}{x ^{2} - 4})

\frac{d}{d t} (t sin (2 t))

\frac{\partial}{\partial v} (v \cdot e^{u (v)})

f (2) = sin (3 x) - 4 x^{4} + 2 x^{3} + 3

What is the derivative of (ln(x)/(2+ln(x))) ?
The derivative of (ln(x)/(2+ln(x))) is 2/(x(2+ln(x))^2)
What is the first derivative of (ln(x)/(2+ln(x))) ?
The first derivative of (ln(x)/(2+ln(x))) is 2/(x(2+ln(x))^2)