What is (\partial)/(\partial x)(12xe^{x-3y}) ?

The answer to (\partial)/(\partial x)(12xe^{x-3y}) is 12(e^{x-3y}+e^{x-3y}x)

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(\partial)/(\partial x)(12xe^{x-3y})

\frac{\partial}{\partial x} (12 x e^{x - 3 y})

12 (e^{x - 3 y} + e^{x - 3 y} x)

Solution steps

\frac{\partial}{\partial x} (12 x e^{x - 3 y})

Treat

y

as a constant

Take the constant out:

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

= 12 \frac{\partial}{\partial x} (x e^{x - 3 y})

Apply the Product Rule:

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

f = x, g = e^{x - 3 y}

= 12 (\frac{\partial}{\partial x} (x) e^{x - 3 y} + \frac{\partial}{\partial x} (e^{x - 3 y}) x)

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

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

= 12 (1 \cdot e^{x - 3 y} + e^{x - 3 y} x)

Simplify

= 12 (e^{x - 3 y} + e^{x - 3 y} x)

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What is (\partial)/(\partial x)(12xe^{x-3y}) ?
The answer to (\partial)/(\partial x)(12xe^{x-3y}) is 12(e^{x-3y}+e^{x-3y}x)