What is (\partial)/(\partial x)(ln(x^2+y^2+6)) ?

The answer to (\partial)/(\partial x)(ln(x^2+y^2+6)) is (2x)/(x^2+y^2+6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(ln(x^2+y^2+6))

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

\frac{2 x}{x ^{2} + y ^{2} + 6}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{2} + y ^{2} + 6} \frac{\partial}{\partial x} (x^{2} + y^{2} + 6)

= \frac{1}{x ^{2} + y ^{2} + 6} \frac{\partial}{\partial x} (x^{2} + y^{2} + 6)

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

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

Simplify

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

= \frac{2 x}{x ^{2} + y ^{2} + 6}

What is (\partial)/(\partial x)(ln(x^2+y^2+6)) ?
The answer to (\partial)/(\partial x)(ln(x^2+y^2+6)) is (2x)/(x^2+y^2+6)