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

The derivative derivative of x^{ln(x}) is (2e^{ln^2(x)}ln(x))/x

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

The first derivative derivative of x^{ln(x}) is (2e^{ln^2(x)}ln(x))/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{d}{d x} (x^{l n (x)})

\frac{2 e ^{l n^{2} (x)} ln ( x )}{x}

Solution steps

\frac{d}{d x} (x^{l n (x)})

Apply exponent rule:

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

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

= \frac{d}{d x} (e^{l n (x) l n (x)})

Apply the chain rule:

e^{l n (x) l n (x)} \frac{d}{d x} (ln (x) ln (x))

= e^{l n (x) l n (x)} \frac{d}{d x} (ln (x) ln (x))

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

= e^{l n (x) l n (x)} \frac{2 ln ( x )}{x}

Simplify

e^{l n (x) l n (x)} \frac{2 ln ( x )}{x} : \frac{2 e ^{l n^{2} (x)} ln ( x )}{x}

= \frac{2 e ^{l n^{2} (x)} ln ( x )}{x}

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

h \to 0 lim (\frac{( f ( x , h ) ( x + h ) - f ( x , h ) x )}{h})

e^{x}

x^{2}

sin (2 x)

What is the derivative derivative of x^{ln(x}) ?
The derivative derivative of x^{ln(x}) is (2e^{ln^2(x)}ln(x))/x
What is the first derivative derivative of x^{ln(x}) ?
The first derivative derivative of x^{ln(x}) is (2e^{ln^2(x)}ln(x))/x