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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= - 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

= - x e^{x y} x

Simplify

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

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

\frac{\partial}{\partial x} (6 x^{7} y^{6} + 2 x^{5} y^{8})

x \to 3 lim (x^{2} - 9)

\int sin (\frac{1}{2} x) d x

3 y^{^{''}} + 11 y^{^{'}} + 6 y = 3 x^{2} + 7 x + 3

\int_{1}^{3} \frac{3 x ^{2} - 7}{x ^{3}} d x

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