What is (\partial)/(\partial x)(3ze^{xy}) ?

The answer to (\partial)/(\partial x)(3ze^{xy}) is 3ze^{xy}y

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(\partial)/(\partial x)(3ze^{xy})

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

3 z e^{x y} y

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

= 3 z \frac{\partial}{\partial x} (e^{x y})

Apply the chain rule:

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

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

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

= 3 z e^{x y} y

(4.5) (2.3)

\frac{d}{d y} (x y z)

\frac{\partial}{\partial x} (- 4 x y (9 - x - y))

\int \frac{3}{2 - t} d t

x \to 0 + lim ((e^{x} + x)^{\frac{1}{4}})

What is (\partial)/(\partial x)(3ze^{xy}) ?
The answer to (\partial)/(\partial x)(3ze^{xy}) is 3ze^{xy}y