What is the derivative of (x+3/x /(sqrt(x))) ?

The derivative of (x+3/x /(sqrt(x))) is (x^2-9)/(2x^2sqrt(x))

What is the first derivative of (x+3/x /(sqrt(x))) ?

The first derivative of (x+3/x /(sqrt(x))) is (x^2-9)/(2x^2sqrt(x))

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\frac{d}{d x} (\frac{x + \frac{3}{x}}{x})

\frac{x ^{2} - 9}{2 x ^{2} x}

Solution steps

\frac{d}{d x} (\frac{x + \frac{3}{x}}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + \frac{3}{x} ) x - \frac{d}{d x} ( x ) ( x + \frac{3}{x} )}{( x ) ^{2}}

\frac{d}{d x} (x + \frac{3}{x}) = 1 - \frac{3}{x ^{2}}

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

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

Simplify

\frac{( 1 - \frac{3}{x ^{2}} ) x - \frac{1}{2 x} ( x + \frac{3}{x} )}{( x ) ^{2}} : \frac{x ^{2} - 9}{2 x ^{2} x}

= \frac{x ^{2} - 9}{2 x ^{2} x}

What is the derivative of (x+3/x /(sqrt(x))) ?
The derivative of (x+3/x /(sqrt(x))) is (x^2-9)/(2x^2sqrt(x))
What is the first derivative of (x+3/x /(sqrt(x))) ?
The first derivative of (x+3/x /(sqrt(x))) is (x^2-9)/(2x^2sqrt(x))