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

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

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

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

e^{x y} y^{2}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= y e^{x y} y

Simplify

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

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

\frac{d}{d x} ((x + \frac{1}{x})^{2})

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

\frac{\partial}{\partial y} (- \frac{1}{y})

\frac{d y}{d t} = y (1 - 0.0002 y)

\int 2^{x} x d x

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