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

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

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

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

3 e^{x - y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 3 \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) = 1

= 3 e^{x - y} \cdot 1

Simplify

= 3 e^{x - y}

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