What is the derivative of ln(x+1/(ln(x))) ?

The derivative of ln(x+1/(ln(x))) is 1/x-1/(xln^2(x))

What is the first derivative of ln(x+1/(ln(x))) ?

The first derivative of ln(x+1/(ln(x))) is 1/x-1/(xln^2(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

x \to 0 lim (1 + 2 x)

\frac{\partial}{\partial x} (x e^{x^{2} y^{2}})

x \to 1 lim (b + \frac{1}{x - 1})

y = 4 x, y = \frac{4}{x}, x = 4

What is the derivative of ln(x+1/(ln(x))) ?
The derivative of ln(x+1/(ln(x))) is 1/x-1/(xln^2(x))
What is the first derivative of ln(x+1/(ln(x))) ?
The first derivative of ln(x+1/(ln(x))) is 1/x-1/(xln^2(x))