What is the derivative of (1+5/x ^x) ?

The derivative of (1+5/x ^x) is (ln(1+5/x)-5/(x+5))(1+5/x)^x

What is the first derivative of (1+5/x ^x) ?

The first derivative of (1+5/x ^x) is (ln(1+5/x)-5/(x+5))(1+5/x)^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} ((1 + \frac{5}{x})^{x})

(ln (1 + \frac{5}{x}) - \frac{5}{x + 5}) (1 + \frac{5}{x})^{x}

Solution steps

\frac{d}{d x} ((1 + \frac{5}{x})^{x})

Apply exponent rule:

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

(1 + \frac{5}{x})^{x} = e^{x l n (1 + \frac{5}{x})}

= \frac{d}{d x} (e^{x l n (1 + \frac{5}{x})})

Apply the chain rule:

e^{x l n (1 + \frac{5}{x})} \frac{d}{d x} (x ln (1 + \frac{5}{x}))

= e^{x l n (1 + \frac{5}{x})} \frac{d}{d x} (x ln (1 + \frac{5}{x}))

\frac{d}{d x} (x ln (1 + \frac{5}{x})) = ln (1 + \frac{5}{x}) - \frac{5}{x + 5}

= e^{x l n (1 + \frac{5}{x})} (ln (1 + \frac{5}{x}) - \frac{5}{x + 5})

e^{x l n (1 + \frac{5}{x})} = (1 + \frac{5}{x})^{x}

= (ln (1 + \frac{5}{x}) - \frac{5}{x + 5}) (1 + \frac{5}{x})^{x}

\frac{\partial}{\partial z} (x e^{2 y + 3 z})

\frac{\partial}{\partial x} (ln (\frac{x}{2 y}))

\int_{0}^{\frac{2}{3}} \frac{1}{4 + 9 x ^{2}} d x

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

\frac{d}{d x} (e^{2 x} sin (7 x))

What is the derivative of (1+5/x ^x) ?
The derivative of (1+5/x ^x) is (ln(1+5/x)-5/(x+5))(1+5/x)^x
What is the first derivative of (1+5/x ^x) ?
The first derivative of (1+5/x ^x) is (ln(1+5/x)-5/(x+5))(1+5/x)^x