What is (\partial)/(\partial x)(2xye^{xz}) ?

The answer to (\partial)/(\partial x)(2xye^{xz}) is 2y(e^{xz}+e^{xz}xz)

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(\partial)/(\partial x)(2xye^{xz})

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

2 y (e^{x z} + e^{x z} x z)

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x z}

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

\frac{\partial}{\partial x} (x) = 1

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

= 2 y (1 \cdot e^{x z} + e^{x z} z x)

Simplify

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

What is (\partial)/(\partial x)(2xye^{xz}) ?
The answer to (\partial)/(\partial x)(2xye^{xz}) is 2y(e^{xz}+e^{xz}xz)