What is (\partial)/(\partial y)(e^{xy}+2x-5y) ?

The answer to (\partial)/(\partial y)(e^{xy}+2x-5y) is e^{xy}x-5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial y)(e^{xy}+2x-5y)

\frac{\partial}{\partial y} (e^{x y} + 2 x - 5 y)

e^{x y} x - 5

Solution steps

\frac{\partial}{\partial y} (e^{x y} + 2 x - 5 y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (e^{x y}) + \frac{\partial}{\partial y} (2 x) - \frac{\partial}{\partial y} (5 y)

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

\frac{\partial}{\partial y} (2 x) = 0

\frac{\partial}{\partial y} (5 y) = 5

= e^{x y} x + 0 - 5

Simplify

= e^{x y} x - 5

What is (\partial)/(\partial y)(e^{xy}+2x-5y) ?
The answer to (\partial)/(\partial y)(e^{xy}+2x-5y) is e^{xy}x-5