What is (\partial)/(\partial z)(x^2yz^2) ?

The answer to (\partial)/(\partial z)(x^2yz^2) is 2x^2yz

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(\partial)/(\partial z)(x^2yz^2)

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

2 x^{2} yz

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 2 x^{2} yz

What is (\partial)/(\partial z)(x^2yz^2) ?
The answer to (\partial)/(\partial z)(x^2yz^2) is 2x^2yz