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

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

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

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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