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

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

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

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

y = (\frac{3 x ^{2}}{2 x + 4})^{3}

\frac{5}{s ( s ^{2} + 5 ^{2} )}

\frac{d}{d x} ((y - c)^{2})

\int cos^{4} (5 x + 4) d x

f (t) = 2 (1 - e^{- 5 t})

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