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Popular >

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

Solution

derivative of

y = \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

limit as x approaches-1-of 2/(x+1)

x \to - 1 - lim (\frac{2}{x + 1})

limit as x approaches-infinity of 4+3/x

x \to - \infty lim (4 + \frac{3}{x})

(\partial)/(\partial x)(2x^y+8y^x+10)

\frac{\partial}{\partial x} (2 x^{y} + 8 y^{x} + 10)

limit as x approaches-2-of sqrt(-1-x)+1

x \to - 2 - lim (- 1 - x + 1)

y^9y^'=11cos(pix)

y^{9} y^{^{'}} = 11 cos (π x)

Frequently Asked Questions (FAQ)

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