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})

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

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

\frac{d P}{d t} = k P^{1.01}, P (0) = 10

\frac{d ^{2}}{d x ^{2}} (cos (5 x))

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