What is the derivative of ((1+sqrt(x)))/x ?

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

What is the first derivative of ((1+sqrt(x)))/x ?

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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