What is (\partial}{\partial x}(\frac{x^{3/2})/3) ?

The answer to (\partial}{\partial x}(\frac{x^{3/2})/3) is (x^{1/2})/2

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(\partial}{\partial x}(\frac{x^{3/2})/3)

\frac{\partial}{\partial x} (\frac{x ^{\frac{3}{2}}}{3})

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

Solution steps

\frac{\partial}{\partial x} (\frac{x ^{\frac{3}{2}}}{3})

Take the constant out:

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

= \frac{1}{3} \frac{\partial}{\partial x} (x^{\frac{3}{2}})

Apply the Power Rule:

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

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

Simplify

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

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

\frac{\partial}{\partial y} (2 x^{2} y + 3 x y^{3})

\int_{0}^{8} x^{3} x^{2} + 64 d x

\frac{\partial}{\partial x} (e^{- 20})

\frac{d}{d x} (2 x^{6} - 9 x^{5} + 15 x^{4} - 10 x^{3} + 3 x - 1)

\frac{d}{d x} (\frac{x ^{2} + x - 12}{x - 4})

What is (\partial}{\partial x}(\frac{x^{3/2})/3) ?
The answer to (\partial}{\partial x}(\frac{x^{3/2})/3) is (x^{1/2})/2