What is the d/(dy)(y^{3/2}) ?

The d/(dy)(y^{3/2}) is (3y^{1/2})/2

What is the first d/(dy)(y^{3/2}) ?

The first d/(dy)(y^{3/2}) is (3y^{1/2})/2

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\frac{d}{d y} (y^{\frac{3}{2}})

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

Solution steps

\frac{d}{d y} (y^{\frac{3}{2}})

Apply the Power Rule:

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

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

Simplify

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

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