What is the derivative of (x^3/(sqrt(x))) ?

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

What is the first derivative of (x^3/(sqrt(x))) ?

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

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

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

Solution steps

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

Simplify

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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