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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

d/(dy)((1/(y^2)-5/(y^4))(y+9y^3))

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 9 y^{3}))

\frac{d y}{d x} = 2 - 3 y

integral from 0 to 1 of 2/((x+2)^2)

\int_{0}^{1} \frac{2}{( x + 2 ) ^{2}} d x

derivative of (1(e^x-e^{-x})/2)

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

integral of (-2)/(5x^2)

\int \frac{- 2}{5 x ^{2}} d x

Frequently Asked Questions (FAQ)

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