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)

\int (cos (x) + 3^{x}) d x

x \to 0 lim (\frac{( 2 - x ) ^{2} + 1}{x})

\frac{d}{d x} (arcsec (7 ln (4 x)))

\int_{- \infty}^{\infty} 15 x e^{- x^{2}} d x

\frac{\partial}{\partial z} (e^{x} cos (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)