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

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

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

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

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

Solution steps

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

Simplify

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

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

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