What is (\partial)/(\partial y)(5x^2-3xy+xyz) ?

The answer to (\partial)/(\partial y)(5x^2-3xy+xyz) is xz-3x

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(\partial)/(\partial y)(5x^2-3xy+xyz)

\frac{\partial}{\partial y} (5 x^{2} - 3 x y + x yz)

x z - 3 x

Solution steps

\frac{\partial}{\partial y} (5 x^{2} - 3 x y + x yz)

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (5 x^{2}) - \frac{\partial}{\partial y} (3 x y) + \frac{\partial}{\partial y} (x yz)

\frac{\partial}{\partial y} (5 x^{2}) = 0

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

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

= 0 - 3 x + x z

Simplify

= x z - 3 x

What is (\partial)/(\partial y)(5x^2-3xy+xyz) ?
The answer to (\partial)/(\partial y)(5x^2-3xy+xyz) is xz-3x