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

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

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

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

e^{x y} y

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= e^{x y} y + 0

Simplify

= e^{x y} y

\int_{- 10}^{10} x^{2} d x

\frac{2}{x}, \frac{1}{2} x, 1, 2

f (x) = (2 x - 8)^{4} (x^{2} + x + 1)^{5}

\frac{d}{d x} (ln (\frac{2 x - 1}{x - 1}))

\frac{d}{d u} (2 u)

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