What is (\partial)/(\partial x)((z)(yx^2-xy)) ?

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

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(\partial)/(\partial x)((z)(yx^2-xy))

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

z (2 y x - y)

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= z (2 y x - y)

(x + ln (x))^{4}

- \frac{3 ( x + 3 ) ( x - 1 )}{x ^{2}}

3 m^{2 (m - n) (2 m + n)}

\frac{x ^{2} + 1}{x ( x - 1 ) ( x + 1 ) ( x - 2 )}

\frac{100 x ^{3} - 600 x ^{2} + 1200 x - 800}{x}

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