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

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

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

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

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derivative

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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