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

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

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

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

\frac{3 y x ^{\frac{1}{2}}}{2}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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