What is (\partial)/(\partial z)(e^{xy}+x^2z) ?

The answer to (\partial)/(\partial z)(e^{xy}+x^2z) is x^2

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(\partial)/(\partial z)(e^{xy}+x^2z)

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

x^{2}

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + x^{2}

Simplify

= x^{2}

x \to 0 - lim (\frac{7}{1 + e ^{\frac{1}{x}}})

\frac{\partial}{\partial x} (x \cdot cos (y) \cdot sin (z))

\int 16 sin^{6} (x) cos^{3} (x) d x

\frac{d}{d x} (\frac{e ^{x}}{x + 4})

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

What is (\partial)/(\partial z)(e^{xy}+x^2z) ?
The answer to (\partial)/(\partial z)(e^{xy}+x^2z) is x^2