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 \frac{cot ^{3} ( x )}{5} d x

\frac{d}{d y} ((\frac{y}{8})^{4} + \frac{1}{4 y ^{2}})

x^{2} y^{^{''}} - 2 y = 0

x \to 1 lim (cos (π) x)

n = 1 \sum \infty 4 (\frac{2}{3})^{n - 1}

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