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

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

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(\partial)/(\partial y)(e^xy)

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

e^{x}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

= e^{x} \cdot 1

Simplify

= e^{x}

\frac{x d y}{d x} + y = \frac{1}{y ^{2}}

f (x) = \frac{x ^{2}}{x + 4}, at x = 2

\frac{d y}{d x} - 2 y = 4 - x

x \to \infty lim (\frac{4 x ^{- 1} - 2 x ^{- 3}}{3 x ^{- 2} + x ^{- 5}})

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