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

The answer to (\partial)/(\partial y)(3x^2y^3) is 9x^2y^2

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

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

9 x^{2} y^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 9 x^{2} y^{2}

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

\int csc (\frac{v - π}{2}) cot (\frac{v - π}{2}) d v

\frac{d y}{d x} + (\frac{4}{x}) y = - 4 x - 5

\int_{0}^{1} \frac{1}{x ( x + 1 )} d x

\frac{\partial}{\partial x} (4 x^{4} y^{5} - 3 x^{2})

What is (\partial)/(\partial y)(3x^2y^3) ?
The answer to (\partial)/(\partial y)(3x^2y^3) is 9x^2y^2