What is (\partial)/(\partial x)(2x+3e^y+xy) ?

The answer to (\partial)/(\partial x)(2x+3e^y+xy) is y+2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(2x+3e^y+xy)

\frac{\partial}{\partial x} (2 x + 3 e^{y} + x y)

y + 2

Solution steps

\frac{\partial}{\partial x} (2 x + 3 e^{y} + x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (2 x) + \frac{\partial}{\partial x} (3 e^{y}) + \frac{\partial}{\partial x} (x y)

\frac{\partial}{\partial x} (2 x) = 2

\frac{\partial}{\partial x} (3 e^{y}) = 0

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

= 2 + 0 + y

Simplify

= y + 2

What is (\partial)/(\partial x)(2x+3e^y+xy) ?
The answer to (\partial)/(\partial x)(2x+3e^y+xy) is y+2