What is (\partial)/(\partial x)(sqrt(8-2x^2-y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(8-2x^2-y^2)) is -(2x)/(sqrt(8-2x^2-y^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(sqrt(8-2x^2-y^2))

\frac{\partial}{\partial x} (8 - 2 x^{2} - y^{2})

- \frac{2 x}{8 - 2 x ^{2} - y ^{2}}

Solution steps

\frac{\partial}{\partial x} (8 - 2 x^{2} - y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 8 - 2 x ^{2} - y ^{2}} \frac{\partial}{\partial x} (8 - 2 x^{2} - y^{2})

= \frac{1}{2 8 - 2 x ^{2} - y ^{2}} \frac{\partial}{\partial x} (8 - 2 x^{2} - y^{2})

\frac{\partial}{\partial x} (8 - 2 x^{2} - y^{2}) = - 4 x

= \frac{1}{2 8 - 2 x ^{2} - y ^{2}} (- 4 x)

Simplify

\frac{1}{2 8 - 2 x ^{2} - y ^{2}} (- 4 x) : - \frac{2 x}{8 - 2 x ^{2} - y ^{2}}

= - \frac{2 x}{8 - 2 x ^{2} - y ^{2}}

What is (\partial)/(\partial x)(sqrt(8-2x^2-y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(8-2x^2-y^2)) is -(2x)/(sqrt(8-2x^2-y^2))