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Popular Calculus >

derivative of (3+2x/(sqrt(x)))

Solution

\frac{d}{d x} (\frac{3 + 2 x}{x})

Solution

\frac{2 x - 3}{2 x x}

Solution steps

\frac{d}{d x} (\frac{3 + 2 x}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 + 2 x ) x - \frac{d}{d x} ( x ) ( 3 + 2 x )}{( x ) ^{2}}

\frac{d}{d x} (3 + 2 x) = 2

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

= \frac{2 x - \frac{1}{2 x} ( 3 + 2 x )}{( x ) ^{2}}

Simplify

\frac{2 x - \frac{1}{2 x} ( 3 + 2 x )}{( x ) ^{2}} : \frac{2 x - 3}{2 x x}

= \frac{2 x - 3}{2 x x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (3+2x/(sqrt(x))) ?
The derivative of (3+2x/(sqrt(x))) is (2x-3)/(2xsqrt(x))
What is the first derivative of (3+2x/(sqrt(x))) ?
The first derivative of (3+2x/(sqrt(x))) is (2x-3)/(2xsqrt(x))