What is the derivative of (sqrt(x^5))/8 ?

The derivative of (sqrt(x^5))/8 is (5x^{3/2})/(16)

What is the first derivative of (sqrt(x^5))/8 ?

The first derivative of (sqrt(x^5))/8 is (5x^{3/2})/(16)

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derivative of

\frac{x ^{5}}{8}

\frac{5 x ^{\frac{3}{2}}}{16}

Solution steps

\frac{d}{d x} (\frac{x ^{5}}{8})

Take the constant out:

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

= \frac{1}{8} \frac{d}{d x} (x^{5})

Apply radical rule:

= \frac{1}{8} \frac{d}{d x} (x^{\frac{5}{2}})

Apply the Power Rule:

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

= \frac{1}{8} \cdot \frac{5}{2} x^{\frac{5}{2} - 1}

Simplify

\frac{1}{8} \cdot \frac{5}{2} x^{\frac{5}{2} - 1} : \frac{5 x ^{\frac{3}{2}}}{16}

= \frac{5 x ^{\frac{3}{2}}}{16}

What is the derivative of (sqrt(x^5))/8 ?
The derivative of (sqrt(x^5))/8 is (5x^{3/2})/(16)
What is the first derivative of (sqrt(x^5))/8 ?
The first derivative of (sqrt(x^5))/8 is (5x^{3/2})/(16)