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

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

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

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

2 x y z^{2}

Solution steps

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

Apply the Power Rule:

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

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

Simplify

= 2 x y z^{2}

\frac{d}{d x} (\frac{3}{x ^{3}} + x^{- 4})

\int \frac{x ^{3}}{1 - 9 x ^{2}} d x

y = \frac{x + 7}{5 x ^{2} e ^{x}}

\int (\frac{4}{x} + e^{2 x}) d x

\int sec (x) sec^{2} (x) d x

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