What is the derivative of (x^2/(sqrt(x))) ?

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

What is the first derivative of (x^2/(sqrt(x))) ?

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

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

\frac{3 x}{2}

Solution steps

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

Simplify

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

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{3 x}{2}

\int_{0}^{1} 2 x^{2} - 1 d x

\frac{d x}{d t} = 2 x (5 - x)

y^{^{'}} = e^{2 y + 6 x}

\int \frac{8 x ^{3} + 8 x ^{2} + 8}{x ^{2} + x} d x

\int \frac{x ln ( x )}{x} d x

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