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Popular >

derivative of (3sqrt(x)/x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

= 3 \cdot \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}}

Simplify

3 \cdot \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}} : - \frac{3}{2 x ^{\frac{3}{2}}}

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

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\int_{5}^{8} \frac{x}{x ^{2} - 2} d x

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Frequently Asked Questions (FAQ)

What is the derivative of (3sqrt(x)/x) ?
The derivative of (3sqrt(x)/x) is -3/(2x^{3/2)}
What is the first derivative of (3sqrt(x)/x) ?
The first derivative of (3sqrt(x)/x) is -3/(2x^{3/2)}