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

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

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

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

3 x^{3} y^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 3 x^{3} y^{2}

\int_{1}^{3} \frac{1}{1 + x ^{2}} d x

arctan (3 x^{2} - 1)

7 y^{^{''}} + y^{^{'}} = 0

n = 1 \sum \infty \frac{9}{n ^{2} + 1}

\int_{1}^{16} \frac{1}{10 + x} d x

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