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

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

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(\partial)/(\partial x)((z)(z^3-z-xy))

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

- zy

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= z (0 - 0 - y)

Simplify

= - zy

\frac{s}{( s ^{2} + 1 ) ( s + 1 ) ^{2} ( s + 2 )}

\frac{d}{d x} \frac{( φ ( x ^{2} + 2 y ( φ , x ) ) + ψ ( φ , x , y ( φ , x ) ) ( x - 2 y ( φ , x ) ^{2} ) )}{x}

\frac{e ^{- 2 π s}}{( s ^{2} + 1 ) \cdot ( s ^{2} - s + 4 )}

\frac{- 2 s ^{4} + 11 s ^{3} + 14 s ^{2} + s + 2}{s ^{2} \cdot ( 1 + 5 s - s ^{3} )}

(3 e^{x} + 2)^{2}

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