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 \cdot 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}

ln (1 - 3 x)

\frac{sec ( x )}{1 + sec ( x )}

\int_{4}^{6} f (x) d x

- \frac{1}{x + 1 ^{2}}

5 + 3 + 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}