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

The derivative of f(x)=(2-ln(x))/(2xsqrt(x)) is (-8+3ln(x))/(4x^{5/2)}

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

The first derivative of f(x)=(2-ln(x))/(2xsqrt(x)) is (-8+3ln(x))/(4x^{5/2)}

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derivative of

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

\frac{- 8 + 3 ln ( x )}{4 x ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x x) = \frac{3 x}{2}

= \frac{1}{2} \cdot \frac{( - \frac{1}{x} ) x x - \frac{3 x}{2} ( 2 - ln ( x ) )}{( x x ) ^{2}}

Simplify

\frac{1}{2} \cdot \frac{( - \frac{1}{x} ) x x - \frac{3 x}{2} ( 2 - ln ( x ) )}{( x x ) ^{2}} : \frac{- 8 + 3 ln ( x )}{4 x ^{\frac{5}{2}}}

= \frac{- 8 + 3 ln ( x )}{4 x ^{\frac{5}{2}}}

y^{^{'''}} - 2 y^{^{''}} - 4 y^{^{'}} + 8 y = 0

\frac{\partial}{\partial y} (- 4 x^{3} + 4 x)

\int_{0}^{\frac{π}{28}} tan (14 x) d x

\frac{d}{d x} (\frac{3 x}{5 y})

\frac{m x}{b x + c}

What is the derivative of f(x)=(2-ln(x))/(2xsqrt(x)) ?
The derivative of f(x)=(2-ln(x))/(2xsqrt(x)) is (-8+3ln(x))/(4x^{5/2)}
What is the first derivative of f(x)=(2-ln(x))/(2xsqrt(x)) ?
The first derivative of f(x)=(2-ln(x))/(2xsqrt(x)) is (-8+3ln(x))/(4x^{5/2)}