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

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

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

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{d}{d x} (\frac{e ^{2 x}}{x ^{2} + 1})

\int_{0}^{1} e^{x} - x e^{x} d x

\int_{x}^{0.5} 8 d y

\frac{d}{d x} (\frac{x}{( x - 1 ) ^{2}})

1 + x, 0

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