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

The derivative of x/(sqrt(x+2)) is (x+4)/(2(x+2)sqrt(x+2))

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

The first derivative of x/(sqrt(x+2)) is (x+4)/(2(x+2)sqrt(x+2))

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derivative of

\frac{x}{x + 2}

\frac{x + 4}{2 ( x + 2 ) x + 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 x}{d x} x + 2 - \frac{d}{d x} ( x + 2 ) x}{( x + 2 ) ^{2}}

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

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

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

Simplify

\frac{1 \cdot x + 2 - \frac{1}{2 x + 2} x}{( x + 2 ) ^{2}} : \frac{x + 4}{2 ( x + 2 ) x + 2}

= \frac{x + 4}{2 ( x + 2 ) x + 2}

\frac{e ^{- s π}}{s ^{2} + 2 s + 2}

\int 7 csc (x) d x

\frac{d}{d x} (2 x - 6)

n = 1 \sum \infty \frac{n}{9 + n}

\frac{9 e ^{9 x}}{8 x + 3}

What is the derivative of x/(sqrt(x+2)) ?
The derivative of x/(sqrt(x+2)) is (x+4)/(2(x+2)sqrt(x+2))
What is the first derivative of x/(sqrt(x+2)) ?
The first derivative of x/(sqrt(x+2)) is (x+4)/(2(x+2)sqrt(x+2))