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

The answer to (\partial)/(\partial x)((z)(xsin(xy)-z)) is z(xycos(xy)+sin(xy))

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(\partial)/(\partial x)((z)(xsin(xy)-z))

\frac{\partial}{\partial x} ((z) (x sin (x y) - z))

z (x y cos (x y) + sin (x y))

Solution steps

\frac{\partial}{\partial x} ((z) (x sin (x y) - z))

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x sin (x y)) = sin (y x) + y x cos (y x)

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

= z (sin (y x) + y x cos (y x) - 0)

Simplify

= z (x y cos (x y) + sin (x y))

(\frac{2 x ^{4}}{3 x})^{3}

\frac{1}{s ( s ^{2} + 3 s + 5 )}

\frac{x ^{2} ( - 10 x ^{3} + 3 x ^{2} - 60 x )}{20}

\frac{d}{d x} ((z) (x^{2} + y^{2} - 2 z^{2} + 12 x - 8 z - 4))

e^{2 (x + 1 - l n ∣ x + 1 ∣)}

What is (\partial)/(\partial x)((z)(xsin(xy)-z)) ?
The answer to (\partial)/(\partial x)((z)(xsin(xy)-z)) is z(xycos(xy)+sin(xy))