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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

4 t (\frac{d y}{d t}) - y = t

\int \frac{1}{144 + x ^{2}} d x

sin (3 x) + cos (4 x)

\int_{0}^{1} \frac{1}{x ^{0.5}} d x

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