What is (\partial)/(\partial y)(x^2yz-xyz^3) ?

The answer to (\partial)/(\partial y)(x^2yz-xyz^3) is x^2z-xz^3

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(\partial)/(\partial y)(x^2yz-xyz^3)

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

x^{2} z - x z^{3}

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

\frac{d}{d y} (\frac{y}{x})

\frac{d}{d x} (\frac{2 x ^{7} + 5 x ^{3} - 1}{4})

\int_{0}^{π} (1 + sin (x)) d x

2 y^{^{'''}} + 3 y^{^{''}} - 23 y^{^{'}} - 12 y = 0

\int x sin (10 x) d x

What is (\partial)/(\partial y)(x^2yz-xyz^3) ?
The answer to (\partial)/(\partial y)(x^2yz-xyz^3) is x^2z-xz^3