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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}}

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}

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

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

Simplify

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

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

Popular Examples

limit as t approaches infinity of 1/t

t \to \infty lim (\frac{1}{t})

integral of (18)/(x^2+1)

\int \frac{18}{x ^{2} + 1} d x

(\partial)/(\partial x)(e^{-6y}cos(6x)*6)

\frac{\partial}{\partial x} (e^{- 6 y} cos (6 x) \cdot 6)

integral of (3x)/(2sqrt(x-1))

\int \frac{3 x}{2 x - 1} d x

derivative of 2^{2x}derivative of

2^{2 x}

Frequently Asked Questions (FAQ)

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