What is (\partial)/(\partial x)(e^{x(e^y)}) ?

The answer to (\partial)/(\partial x)(e^{x(e^y)}) is e^{e^yx+y}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(e^{x(e^y)})

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

e^{e^{y} x + y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{x e^{y}} e^{y}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{x e^{y}} e^{y} = e^{e^{y} x + y}

= e^{e^{y} x + y}

2 (x - 2) - cos (3 x) \cdot 3

\int - e^{- t} d t

\frac{d}{d x} (arcsec (2 x))

x \to 2 lim (x^{2} + 3)

\int_{- 2}^{2} (2 4 - x^{2})^{2} d x

What is (\partial)/(\partial x)(e^{x(e^y)}) ?
The answer to (\partial)/(\partial x)(e^{x(e^y)}) is e^{e^yx+y}