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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= - 2 \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}

= - 2 (\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

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

Simplify

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

x \to 1 lim (101)

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

\int_{0}^{1} 6 (1 + x)^{6} d x

4 sin (x)

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