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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (x^{2} - y) = - 1

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

Simplify

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

\int (3 x + 1)^{7} d x

x \to - 6 + lim (\frac{x + 7}{x + 6})

\frac{\partial}{\partial y} (cos (x y) x)

\frac{d}{d x} ((x^{2} - \frac{2}{3})^{\frac{3}{2}})

\frac{7}{ln ( x )}

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