What is (\partial)/(\partial y)(6y^{3/2}) ?

The answer to (\partial)/(\partial y)(6y^{3/2}) is 9y^{1/2}

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(\partial)/(\partial y)(6y^{3/2})

\frac{\partial}{\partial y} (6 y^{\frac{3}{2}})

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

Solution steps

\frac{\partial}{\partial y} (6 y^{\frac{3}{2}})

Take the constant out:

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

= 6 \frac{\partial}{\partial y} (y^{\frac{3}{2}})

Apply the Power Rule:

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

= 6 \cdot \frac{3}{2} y^{\frac{3}{2} - 1}

Simplify

6 \cdot \frac{3}{2} y^{\frac{3}{2} - 1} : 9 y^{\frac{1}{2}}

= 9 y^{\frac{1}{2}}

x \to 6 lim (\frac{x}{x ^{2} + 8})

\int_{- 1}^{3} \frac{x}{∣ x ∣} d x

\frac{d}{d x} (\frac{cos ( x )}{x ^{2} + tan ( x )})

x \to 7 + lim (\frac{8}{7 - x})

f (t) = \frac{2}{3} t^{3} e^{- 8 t}

What is (\partial)/(\partial y)(6y^{3/2}) ?
The answer to (\partial)/(\partial y)(6y^{3/2}) is 9y^{1/2}