What is (\partial)/(\partial y)(x*e^{x*y}) ?

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

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

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

y^{^{''}} - 2 y^{^{'}} + y = 8 e^{x}

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

sec^{2} (x) + tan^{2} (x)

f (x) = 15 x - 1.86 x^{2}, at x = a

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