What is (\partial)/(\partial x)((z)(e^{2z}-xyz)) ?

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

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(\partial)/(\partial x)((z)(e^{2z}-xyz))

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

- z^{2} y

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (e^{2 z}) = 0

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

= z (0 - zy)

Simplify

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

= - z^{2} y

\frac{3 ( x - 1 )}{4}

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

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

\frac{( 0.675 + 2 x ) ^{2}}{( 0.5643 - x ) ( 0.7653 - x )}

(x - 2) (x - 3) (x - 5) (x + 5)

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