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Popular >

derivative of (ln(x)/(sqrt(x)))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial y)(9x^y+2y^x+11)

\frac{\partial}{\partial y} (9 x^{y} + 2 y^{x} + 11)

integral of (3t-2)/(sqrt(9-t^2))

\int \frac{3 t - 2}{9 - t ^{2}} d t

integral of arcsec(x)

\int arcsec (x) d x

derivative of x/(ax^2+b)

\frac{d}{d x} (\frac{x}{a x ^{2} + b})

limit as x approaches-4-of x^2+5/(x+4)

x \to - 4 - lim (x^{2} + \frac{5}{x + 4})

Frequently Asked Questions (FAQ)

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