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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= - 2 x e^{x y} x

Simplify

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

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

y^{^{'}} = (x - 14)^{2}

y^{^{''}} + 324 y = sec (18 x), y (0) = 2, y^{^{'}} (0) = - 1

n = 3 \sum \infty \frac{3}{n ^{2} - 3 n + 2}

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

\int \frac{( ln ( x ) ) ^{2} + 1}{ln ( x )} d x

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