en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(x^x)^'

Solution

(x^{x})^{^{'}}

Solution

x^{x} (ln (x) + 1)

Solution steps

(x^{x})^{'}

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{x} = e^{x l n (x)}

= (e^{x l n (x)})^{^{'}}

Apply the chain rule:

e^{x l n (x)} (x ln (x))^{'}

= e^{x l n (x)} (x ln (x))^{'}

(x ln (x))^{'} = ln (x) + 1

= e^{x l n (x)} (ln (x) + 1)

e^{x l n (x)} = x^{x}

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

Popular Examples

limit as x approaches 2-of ln(4-2x)

x \to 2 - lim (ln (4 - 2 x))

integral of tan^2(t)sec^3(t)

\int tan^{2} (t) sec^{3} (t) d t

sum from n=0 to infinity of 5^{-n}

n = 0 \sum \infty 5^{- n}

derivative of ln(1+8x)

\frac{d}{d x} (ln (1 + 8 x))

limit as x approaches 1+of 1/(x^2+1)

x \to 1 + lim (\frac{1}{x ^{2} + 1})

Frequently Asked Questions (FAQ)

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