What is the derivative of y=ln(ln(sqrt(x))) ?

The derivative of y=ln(ln(sqrt(x))) is 1/(2xln(sqrt(x)))

What is the first derivative of y=ln(ln(sqrt(x))) ?

The first derivative of y=ln(ln(sqrt(x))) is 1/(2xln(sqrt(x)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = ln (ln (x))

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

Solution steps

\frac{d}{d x} (ln (ln (x)))

Apply the chain rule:

\frac{1}{ln ( x )} \frac{d}{d x} (ln (x))

= \frac{1}{ln ( x )} \frac{d}{d x} (ln (x))

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

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

Simplify

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

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

What is the derivative of y=ln(ln(sqrt(x))) ?
The derivative of y=ln(ln(sqrt(x))) is 1/(2xln(sqrt(x)))
What is the first derivative of y=ln(ln(sqrt(x))) ?
The first derivative of y=ln(ln(sqrt(x))) is 1/(2xln(sqrt(x)))