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Popular >

derivative of ((1+sqrt(x)))/x

Solution

derivative of

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

Solution

\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}}

Popular Examples

integral of (y+3)/((3-y)^{2/3)}

\int \frac{y + 3}{( 3 - y ) ^{\frac{2}{3}}} d y

area y= 1/(x^2+1),x=0,x=6,y=0 area

y = \frac{1}{x ^{2} + 1}, x = 0, x = 6, y = 0

derivative of-6x^2+5

\frac{d}{d x} (- 6 x^{2} + 5)

derivative of arccos(x-1)

\frac{d}{d x} (arccos (x - 1))

integral from-15 to 0 of 1/(sqrt(1-x))

\int_{- 15}^{0} \frac{1}{1 - x} d x

Frequently Asked Questions (FAQ)

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)