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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

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