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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = e^{x - 2 z}

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

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

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

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

Simplify

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

\frac{\partial}{\partial x} (A + B \cdot cos (x) sin (y))

\frac{d x}{d t} = x^{\frac{2}{3}}

\frac{1}{4 s ^{2}}

y^{^{'}} - y = 3 t e^{2 t}, y (0) = 1

2 sin (t)

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