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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\frac{d}{d x} (\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}}

\int_{3}^{6} 21 - \frac{x ^{2}}{2} d x

\int \frac{1}{7 - x ^{2}} d x

\int_{0}^{2} \frac{x - 2}{x - 1} d x

\int \frac{x ^{2}}{8 - x} d x

(x^{2} + 15)^{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)