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

The answer to (\partial)/(\partial x)(ln(ln(2x+2y))) is 1/(ln(2x+2y)(x+y))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{1}{ln ( 2 x + 2 y ) ( x + y )}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{ln ( 2 x + 2 y )} \cdot \frac{1}{x + y}

Simplify

\frac{1}{ln ( 2 x + 2 y )} \cdot \frac{1}{x + y} : \frac{1}{ln ( 2 x + 2 y ) ( x + y )}

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

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