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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(sqrt(3x^2+3y^2))

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

\frac{3 x}{3 x ^{2} + 3 y ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 3 x ^{2} + 3 y ^{2}} \frac{\partial}{\partial x} (3 x^{2} + 3 y^{2})

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

\frac{\partial}{\partial x} (3 x^{2} + 3 y^{2}) = 6 x

= \frac{1}{2 3 x ^{2} + 3 y ^{2}} \cdot 6 x

Simplify

\frac{1}{2 3 x ^{2} + 3 y ^{2}} \cdot 6 x : \frac{3 x}{3 x ^{2} + 3 y ^{2}}

= \frac{3 x}{3 x ^{2} + 3 y ^{2}}

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