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 + 7 lim (\frac{x}{x + 7})

\frac{\partial}{\partial x} (\frac{x e ^{y}}{3 z ^{2} + 1})

\frac{d y}{d x} + 3 x y^{3} = 0, y (0) = 1

\int \frac{5 e ^{2 x} - e ^{x}}{e ^{2 x} - 1} d x

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