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Popular >

derivative of x/(sqrt(x+8))

Solution

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

Solution

\frac{x + 16}{2 ( x + 8 ) x + 8}

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

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

\frac{d}{d x} (x + 8) = \frac{1}{2 x + 8}

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

Simplify

\frac{1 \cdot x + 8 - \frac{1}{2 x + 8} x}{( x + 8 ) ^{2}} : \frac{x + 16}{2 ( x + 8 ) x + 8}

= \frac{x + 16}{2 ( x + 8 ) x + 8}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of x/(sqrt(x+8)) ?
The derivative of x/(sqrt(x+8)) is (x+16)/(2(x+8)sqrt(x+8))
What is the first derivative of x/(sqrt(x+8)) ?
The first derivative of x/(sqrt(x+8)) is (x+16)/(2(x+8)sqrt(x+8))