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

The derivative of f(x)=(ln(x))/(sqrt(x)) is (2-ln(x))/(2xsqrt(x))

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

The first derivative of f(x)=(ln(x))/(sqrt(x)) is (2-ln(x))/(2xsqrt(x))

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derivative of

f (x) = \frac{ln ( x )}{x}

\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}

y = 5 arctan (x - 1 + x^{2})

\frac{d}{d x} ((1 + sin (x)) sin (x))

y^{^{'}} = (x - 1) e^{x}

\frac{0.3 ( 9 ^{x} )}{x ^{3}}

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

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