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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

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