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Popular >

derivative of (2x^{5/2}/5)

Solution

\frac{d}{d x} (\frac{2 x ^{\frac{5}{2}}}{5})

Solution

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

Solution steps

\frac{d}{d x} (\frac{2 x ^{\frac{5}{2}}}{5})

Take the constant out:

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

= \frac{2}{5} \frac{d}{d x} (x^{\frac{5}{2}})

Apply the Power Rule:

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

= \frac{2}{5} \cdot \frac{5}{2} x^{\frac{5}{2} - 1}

Simplify

\frac{2}{5} \cdot \frac{5}{2} x^{\frac{5}{2} - 1} : x^{\frac{3}{2}}

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

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Frequently Asked Questions (FAQ)

What is the derivative of (2x^{5/2}/5) ?
The derivative of (2x^{5/2}/5) is x^{3/2}
What is the first derivative of (2x^{5/2}/5) ?
The first derivative of (2x^{5/2}/5) is x^{3/2}