What is the derivative of (sqrt(x))/(x+6) ?

The derivative of (sqrt(x))/(x+6) is (-x+6)/(2sqrt(x)(x+6)^2)

What is the first derivative of (sqrt(x))/(x+6) ?

The first derivative of (sqrt(x))/(x+6) is (-x+6)/(2sqrt(x)(x+6)^2)

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derivative of

\frac{x}{x + 6}

\frac{- x + 6}{2 x ( x + 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x + 6})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ) ( x + 6 ) - \frac{d}{d x} ( x + 6 ) x}{( x + 6 ) ^{2}}

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

\frac{d}{d x} (x + 6) = 1

= \frac{\frac{1}{2 x} ( x + 6 ) - 1 \cdot x}{( x + 6 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x + 6 ) - 1 \cdot x}{( x + 6 ) ^{2}} : \frac{- x + 6}{2 x ( x + 6 ) ^{2}}

= \frac{- x + 6}{2 x ( x + 6 ) ^{2}}

What is the derivative of (sqrt(x))/(x+6) ?
The derivative of (sqrt(x))/(x+6) is (-x+6)/(2sqrt(x)(x+6)^2)
What is the first derivative of (sqrt(x))/(x+6) ?
The first derivative of (sqrt(x))/(x+6) is (-x+6)/(2sqrt(x)(x+6)^2)