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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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