What is (\partial)/(\partial y)(x^3y^6) ?

The answer to (\partial)/(\partial y)(x^3y^6) is 6x^3y^5

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(\partial)/(\partial y)(x^3y^6)

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

6 x^{3} y^{5}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= x^{3} \cdot 6 y^{6 - 1}

Simplify

= 6 x^{3} y^{5}

What is (\partial)/(\partial y)(x^3y^6) ?
The answer to (\partial)/(\partial y)(x^3y^6) is 6x^3y^5