What is (\partial)/(\partial x)(1/(x^2)+1/(y^2)) ?

The answer to (\partial)/(\partial x)(1/(x^2)+1/(y^2)) is -2/(x^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(1/(x^2)+1/(y^2))

\frac{\partial}{\partial x} (\frac{1}{x ^{2}} + \frac{1}{y ^{2}})

- \frac{2}{x ^{3}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x ^{2}} + \frac{1}{y ^{2}})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (\frac{1}{x ^{2}}) + \frac{\partial}{\partial x} (\frac{1}{y ^{2}})

\frac{\partial}{\partial x} (\frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

\frac{\partial}{\partial x} (\frac{1}{y ^{2}}) = 0

= - \frac{2}{x ^{3}} + 0

Simplify

= - \frac{2}{x ^{3}}

What is (\partial)/(\partial x)(1/(x^2)+1/(y^2)) ?
The answer to (\partial)/(\partial x)(1/(x^2)+1/(y^2)) is -2/(x^3)