What is (\partial)/(\partial x)(x^{ln(x)}) ?

The answer to (\partial)/(\partial x)(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 >

(\partial)/(\partial x)(x^{ln(x)})

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

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

Solution steps

\frac{\partial}{\partial 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{\partial}{\partial x} (e^{l n (x) l n (x)})

Apply the chain rule:

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

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

\frac{\partial}{\partial 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}

\int_{- 2}^{2} 2 x^{2} - 6 x + 14 d x

\int x^{2} - 2 x + 8 d x

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

x \to \infty lim (\frac{n !}{n})

\int \frac{x + 1}{x ^{2} + 4 x + 3} d x

What is (\partial)/(\partial x)(x^{ln(x)}) ?
The answer to (\partial)/(\partial x)(x^{ln(x)}) is (2e^{ln^2(x)}ln(x))/x