What is (\partial)/(\partial x)(9/x+3/y+xy) ?

The answer to (\partial)/(\partial x)(9/x+3/y+xy) is y-9/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(9/x+3/y+xy)

\frac{\partial}{\partial x} (\frac{9}{x} + \frac{3}{y} + x y)

y - \frac{9}{x ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{9}{x} + \frac{3}{y} + x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (\frac{9}{x}) + \frac{\partial}{\partial x} (\frac{3}{y}) + \frac{\partial}{\partial x} (x y)

\frac{\partial}{\partial x} (\frac{9}{x}) = - \frac{9}{x ^{2}}

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

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

= - \frac{9}{x ^{2}} + 0 + y

Simplify

= y - \frac{9}{x ^{2}}

What is (\partial)/(\partial x)(9/x+3/y+xy) ?
The answer to (\partial)/(\partial x)(9/x+3/y+xy) is y-9/(x^2)