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Popular Calculus >

derivative of (x+9)/(sqrt(x))

Solution

derivative of

\frac{x + 9}{x}

Solution

\frac{x - 9}{2 x x}

Solution steps

\frac{d}{d x} (\frac{x + 9}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 9 ) x - \frac{d}{d x} ( x ) ( x + 9 )}{( x ) ^{2}}

\frac{d}{d x} (x + 9) = 1

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

= \frac{1 \cdot x - \frac{1}{2 x} ( x + 9 )}{( x ) ^{2}}

Simplify

\frac{1 \cdot x - \frac{1}{2 x} ( x + 9 )}{( x ) ^{2}} : \frac{x - 9}{2 x x}

= \frac{x - 9}{2 x x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (x+9)/(sqrt(x)) ?
The derivative of (x+9)/(sqrt(x)) is (x-9)/(2xsqrt(x))
What is the first derivative of (x+9)/(sqrt(x)) ?
The first derivative of (x+9)/(sqrt(x)) is (x-9)/(2xsqrt(x))