What is the derivative of (sqrt(x))/(x+2) ?

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

What is the first derivative of (sqrt(x))/(x+2) ?

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

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derivative of

\frac{x}{x + 2}

\frac{- x + 2}{2 x ( x + 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

y^{^{'}} = y^{2} + x y^{2}

\int \frac{7}{x ( x ^{4} + 6 )} d x

k = 1 \sum \infty \frac{1}{2 ^{k}}

3 x + y - 2 + \frac{d y}{d x} (x - 1) = 0

n = 0 \sum \infty \frac{1}{2 n + 1}

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