What is (\partial)/(\partial x)(-3xe^{2xy}) ?

The answer to (\partial)/(\partial x)(-3xe^{2xy}) is -3(e^{2xy}+2e^{2xy}xy)

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(\partial)/(\partial x)(-3xe^{2xy})

\frac{\partial}{\partial x} (- 3 x e^{2 x y})

- 3 (e^{2 x y} + 2 e^{2 x y} x y)

Solution steps

\frac{\partial}{\partial x} (- 3 x e^{2 x y})

Treat

y

as a constant

Take the constant out:

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

= - 3 \frac{\partial}{\partial x} (x e^{2 x y})

Apply the Product Rule:

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

f = x, g = e^{2 x y}

= - 3 (\frac{\partial}{\partial x} (x) e^{2 x y} + \frac{\partial}{\partial x} (e^{2 x y}) x)

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

\frac{\partial}{\partial x} (e^{2 x y}) = e^{2 x y} \cdot 2 y

= - 3 (1 \cdot e^{2 x y} + e^{2 x y} \cdot 2 y x)

Simplify

= - 3 (e^{2 x y} + 2 e^{2 x y} x y)

What is (\partial)/(\partial x)(-3xe^{2xy}) ?
The answer to (\partial)/(\partial x)(-3xe^{2xy}) is -3(e^{2xy}+2e^{2xy}xy)