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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

y = \frac{3 x}{sin ( x )}

x \to - 1 lim (6 - 3 x)

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

\int_{0}^{2} [(- x^{2} + 4 x) - x^{2}] d x

\frac{d}{d x} (1 - \frac{9}{x ^{2}})

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