What is (\partial)/(\partial x)(2xe^{8xy}) ?

The answer to (\partial)/(\partial x)(2xe^{8xy}) is 2(e^{8xy}+8e^{8xy}xy)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(2xe^{8xy})

\frac{\partial}{\partial x} (2 x e^{8 x y})

2 (e^{8 x y} + 8 e^{8 x y} x y)

Solution steps

\frac{\partial}{\partial x} (2 x e^{8 x y})

Treat

y

as a constant

Take the constant out:

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

= 2 \frac{\partial}{\partial x} (x e^{8 x y})

Apply the Product Rule:

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

f = x, g = e^{8 x y}

= 2 (\frac{\partial}{\partial x} (x) e^{8 x y} + \frac{\partial}{\partial x} (e^{8 x y}) x)

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

\frac{\partial}{\partial x} (e^{8 x y}) = e^{8 x y} \cdot 8 y

= 2 (1 \cdot e^{8 x y} + e^{8 x y} \cdot 8 y x)

Simplify

= 2 (e^{8 x y} + 8 e^{8 x y} x y)

x \to 0 lim (\frac{9 ^{x} - 1 0 ^{x}}{x})

z \to (1 - i) lim (x + i (2 x + y))

\frac{x}{x ^{2} + 16}

What is (\partial)/(\partial x)(2xe^{8xy}) ?
The answer to (\partial)/(\partial x)(2xe^{8xy}) is 2(e^{8xy}+8e^{8xy}xy)