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

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

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(\partial)/(\partial y)(e^{xy}x)

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

e^{x y} x^{2}

Solution steps

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

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{( - 10 x - 9 y x ^{2} )}{3 ( x ^{3} - 5 y ^{2} )}

\int x \cdot cos (2 x) d x

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

x^{4} + 9 x^{2} - x (1.9)

f (x) = x^{2} + 2, at x = - 1

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