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

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

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(\partial)/(\partial y)(xy^3z^2)

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

3 x y^{2} z^{2}

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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