What is the derivative of (6x^{3/2}/x) ?

The derivative of (6x^{3/2}/x) is 3/(x^{1/2)}

What is the first derivative of (6x^{3/2}/x) ?

The first derivative of (6x^{3/2}/x) is 3/(x^{1/2)}

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\frac{d}{d x} (\frac{6 x ^{\frac{3}{2}}}{x})

\frac{3}{x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (\frac{6 x ^{\frac{3}{2}}}{x})

Simplify

\frac{6 x ^{\frac{3}{2}}}{x} : 6 x^{\frac{1}{2}}

= \frac{d}{d x} (6 x^{\frac{1}{2}})

Take the constant out:

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

= 6 \frac{d}{d x} (x^{\frac{1}{2}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 6 \cdot \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

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

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

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What is the derivative of (6x^{3/2}/x) ?
The derivative of (6x^{3/2}/x) is 3/(x^{1/2)}
What is the first derivative of (6x^{3/2}/x) ?
The first derivative of (6x^{3/2}/x) is 3/(x^{1/2)}