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

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

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

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

e^{x y} y

Solution steps

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

Treat

y

as a constant

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

= e^{x y} y

\frac{d}{d x} (e^{- x} sin (π) x)

(8 x)^{6 x}

6 x e^{- x^{2}}

x \to \infty lim (- e^{2 x})

y^{^{'}} = x + y, y (0) = 3

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