What is the derivative of (sqrt(x)/(x+8)) ?

The derivative of (sqrt(x)/(x+8)) is (-x+8)/(2sqrt(x)(x+8)^2)

What is the first derivative of (sqrt(x)/(x+8)) ?

The first derivative of (sqrt(x)/(x+8)) is (-x+8)/(2sqrt(x)(x+8)^2)

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\frac{d}{d x} (\frac{x}{x + 8})

\frac{- x + 8}{2 x ( x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ) ( x + 8 ) - \frac{d}{d x} ( x + 8 ) x}{( x + 8 ) ^{2}}

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

\frac{d}{d x} (x + 8) = 1

= \frac{\frac{1}{2 x} ( x + 8 ) - 1 \cdot x}{( x + 8 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x + 8 ) - 1 \cdot x}{( x + 8 ) ^{2}} : \frac{- x + 8}{2 x ( x + 8 ) ^{2}}

= \frac{- x + 8}{2 x ( x + 8 ) ^{2}}

\int 3 - x^{2} d x

\frac{1}{s ^{2} + 7 s}

\int 1 + e^{- x} d x

x \to 0 lim (\frac{a}{x})

n = 0 \sum \infty (2 n)! (\frac{x}{7})^{n}

What is the derivative of (sqrt(x)/(x+8)) ?
The derivative of (sqrt(x)/(x+8)) is (-x+8)/(2sqrt(x)(x+8)^2)
What is the first derivative of (sqrt(x)/(x+8)) ?
The first derivative of (sqrt(x)/(x+8)) is (-x+8)/(2sqrt(x)(x+8)^2)