What is (\partial)/(\partial x)((z)(sin(z)-xyz)) ?

The answer to (\partial)/(\partial x)((z)(sin(z)-xyz)) is -z^2y

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(\partial)/(\partial x)((z)(sin(z)-xyz))

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

- z^{2} y

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (x yz) = zy

= z (0 - zy)

Simplify

z (0 - zy) : - z^{2} y

= - z^{2} y

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

- 3 (5 + 7)

a (1, - 3) b (5, 6)

5 (sin (x) + x cos (x))

\frac{( n + 1 ) ^{4} + 2 ( n + 1 ) ^{3} + ( n + 1 ) ^{2}}{4}

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