What is (\partial)/(\partial x)(e^z(x-y)^2) ?

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

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(\partial)/(\partial x)(e^z(x-y)^2)

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

2 e^{z} (x - y)

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the chain rule:

2 (x - y) \frac{\partial}{\partial x} (x - y)

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

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

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

Simplify

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

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