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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{x ^{3}}{1 - x ^{3}})

\frac{\partial}{\partial x} (x + e^{z} + y)

\int 4 sin (2 x) - 3 cos (3 x) d x

f (x) = x^{4} + 5 x - 2, (1, 4)

\int \frac{e ^{4 r}}{r} d r

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