What is the derivative of ln(ln(x/(2-x^2))) ?

The derivative of ln(ln(x/(2-x^2))) is (2+x^2)/(xln(x/(2-x^2))(-x^2+2))

What is the first derivative of ln(ln(x/(2-x^2))) ?

The first derivative of ln(ln(x/(2-x^2))) is (2+x^2)/(xln(x/(2-x^2))(-x^2+2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

ln (ln (\frac{x}{2 - x ^{2}}))

\frac{2 + x ^{2}}{x ln ( \frac{x}{2 - x ^{2}} ) ( - x ^{2} + 2 )}

Solution steps

\frac{d}{d x} (ln (ln (\frac{x}{2 - x ^{2}})))

Apply the chain rule:

\frac{1}{ln ( \frac{x}{2 - x ^{2}} )} \frac{d}{d x} (ln (\frac{x}{2 - x ^{2}}))

= \frac{1}{ln ( \frac{x}{2 - x ^{2}} )} \frac{d}{d x} (ln (\frac{x}{2 - x ^{2}}))

\frac{d}{d x} (ln (\frac{x}{2 - x ^{2}})) = \frac{2 + x ^{2}}{x ( - x ^{2} + 2 )}

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

Simplify

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

= \frac{2 + x ^{2}}{x ln ( \frac{x}{2 - x ^{2}} ) ( - x ^{2} + 2 )}

What is the derivative of ln(ln(x/(2-x^2))) ?
The derivative of ln(ln(x/(2-x^2))) is (2+x^2)/(xln(x/(2-x^2))(-x^2+2))
What is the first derivative of ln(ln(x/(2-x^2))) ?
The first derivative of ln(ln(x/(2-x^2))) is (2+x^2)/(xln(x/(2-x^2))(-x^2+2))