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

The derivative of (x+sqrt(x)/x) is -1/(2x^{3/2)}

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

The first derivative of (x+sqrt(x)/x) is -1/(2x^{3/2)}

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

- \frac{1}{2 x ^{\frac{3}{2}}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d x}{d x} = 1

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

Simplify

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

= - \frac{1}{2 x ^{\frac{3}{2}}}

What is the derivative of (x+sqrt(x)/x) ?
The derivative of (x+sqrt(x)/x) is -1/(2x^{3/2)}
What is the first derivative of (x+sqrt(x)/x) ?
The first derivative of (x+sqrt(x)/x) is -1/(2x^{3/2)}