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

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

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(\partial)/(\partial y)(xe^{yx})

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

e^{x y} x^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x e^{y x} x

Simplify

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

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

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

\frac{\partial}{\partial x} ((2 x - y)^{4})

\int_{0}^{π} (π - x) cos (n x) d x

x \to 6 lim (x - 10)

y^{^{''}} + 5 y^{^{'}} - 6 y = 0

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