What is (\partial)/(\partial x)((z)(xy+z^3x-2yz)) ?

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

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(\partial)/(\partial x)((z)(xy+z^3x-2yz))

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

z (z^{3} + y)

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (2 yz) = 0

= z (y + z^{3} - 0)

Simplify

= z (z^{3} + y)

(e^{x} - x)^{2}

(2 x - 1) 2 x - 1

\frac{4 e ^{- 2 s} - 4 - 2 s}{s ( s + 2 )}

(x + 2) (x - 3) (x + 3)

(x - 2) (x + 3) (x - 3)

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