What is (\partial)/(\partial x)(e^{(x^2-y^2)}) ?

The answer to (\partial)/(\partial x)(e^{(x^2-y^2)}) is e^{x^2-y^2}*2x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

e^{x^{2} - y^{2}} \cdot 2 x

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{x^{2} - y^{2}} \cdot 2 x

What is (\partial)/(\partial x)(e^{(x^2-y^2)}) ?
The answer to (\partial)/(\partial x)(e^{(x^2-y^2)}) is e^{x^2-y^2}*2x