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

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

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

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

zy

Solution steps

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

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

\frac{\partial}{\partial x} (z^{3}) = 0

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

= z (y + 0 - 0)

Simplify

= zy

\frac{4 s + 5}{( s + 3 ) ^{2}}

(2 x y + 3) d x

\frac{5}{x ( x + 5 )}

\frac{2 s}{- 2 s ^{2} + 1 + 4 s ^{4}}

e^{2 (t - 1)} cos (w) (t - 1) H (t - 1)

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