What is (\partial)/(\partial x)(xe^{-3xy}) ?

The answer to (\partial)/(\partial x)(xe^{-3xy}) is e^{-3xy}-3e^{-3xy}xy

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(\partial)/(\partial x)(xe^{-3xy})

\frac{\partial}{\partial x} (x e^{- 3 x y})

e^{- 3 x y} - 3 e^{- 3 x y} x y

Solution steps

\frac{\partial}{\partial x} (x e^{- 3 x y})

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{- 3 x y}

= \frac{\partial}{\partial x} (x) e^{- 3 x y} + \frac{\partial}{\partial x} (e^{- 3 x y}) x

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

\frac{\partial}{\partial x} (e^{- 3 x y}) = - 3 y e^{- 3 y x}

= 1 \cdot e^{- 3 x y} + (- 3 y e^{- 3 y x}) x

Simplify

= e^{- 3 x y} - 3 e^{- 3 x y} x y

n = 1 \sum \infty \frac{n}{3}

\frac{d}{d x} (\frac{3 x - 4}{6 x ^{2} - 1})

f (x) = ln (5 x - 7)

\int \frac{x ^{2} + 9}{x ^{2} + 4} d x

\int \frac{1}{7 y} d y

What is (\partial)/(\partial x)(xe^{-3xy}) ?
The answer to (\partial)/(\partial x)(xe^{-3xy}) is e^{-3xy}-3e^{-3xy}xy