What is the derivative of ln(x^x) ?

The derivative of ln(x^x) is ln(x)+1

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

The first derivative of ln(x^x) is ln(x)+1

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^{x}))

ln (x) + 1

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= ln (x) + 1

\int 4 x e^{- 2 x^{2}} d x

\frac{d}{d x} ((cos (x) + 2)^{3})

\int \frac{4 x}{( x ^{2} + 6 ) ^{2}} d x

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

\frac{d}{d x} (- \frac{2}{9 x ^{\frac{5}{3}}})

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