What is (\partial)/(\partial x)((z)(x^2y+yz^2-xz)) ?

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

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(\partial)/(\partial x)((z)(x^2y+yz^2-xz))

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

z (2 x y - z)

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= z (2 y x + 0 - z)

Simplify

= z (2 x y - z)

2 (2 y^{3} + 3 y^{2} - 5 y - 4)^{2}

f^{'} (x) (1 - 3 x^{2})^{3}

\frac{d ^{2}}{d x ^{2}} ((y) (x + y))

- 32 (1 - 37) + \frac{- 16 - 272 37}{27}

(n + 2 i - n + i) n

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