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

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

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

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

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\frac{d}{d 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}}}

cos (2 π t)

t^{2} y^{^{''}} - 6 t y^{^{'}} + 10 y = 0

\frac{d}{d x} (ln (x^{5} (x + 4)^{7} (x^{2} + 4)^{5}))

\int_{0}^{4} x + 2 - x d x

\int \frac{y ^{2} + 16}{y} d y

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