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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{y ^{^{'}} - e ^{- t} + 3}{y} = - 3, y (0) = 4

y^{^{''}} - 3 y^{^{'}} - 4 y = 2 sin (t)

\frac{d}{d x} (5 x cos (x))

x \to 0 + lim (3 - x)

\frac{d}{d x} (3 sin (x) + 3 cos (x))

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