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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int 30 t^{5} e^{- t^{6}} d t

\frac{d}{d x} (\frac{x}{9 + x})

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

\int \frac{( e ^{2 x} )}{4 + e ^{4 x}} d x

\int l d l

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