What is the derivative of (x+1^{2x}) ?

The derivative of (x+1^{2x}) is 2(ln(x+1)+x/(x+1))(x+1)^{2x}

What is the first derivative of (x+1^{2x}) ?

The first derivative of (x+1^{2x}) is 2(ln(x+1)+x/(x+1))(x+1)^{2x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

2 (ln (x + 1) + \frac{x}{x + 1}) (x + 1)^{2 x}

Solution steps

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

Apply exponent rule:

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

(x + 1)^{2 x} = e^{2 x l n (x + 1)}

= \frac{d}{d x} (e^{2 x l n (x + 1)})

Apply the chain rule:

e^{2 x l n (x + 1)} \frac{d}{d x} (2 x ln (x + 1))

= e^{2 x l n (x + 1)} \frac{d}{d x} (2 x ln (x + 1))

\frac{d}{d x} (2 x ln (x + 1)) = 2 (ln (x + 1) + \frac{x}{x + 1})

= e^{2 x l n (x + 1)} \cdot 2 (ln (x + 1) + \frac{x}{x + 1})

e^{2 x l n (x + 1)} = (x + 1)^{2 x}

= 2 (ln (x + 1) + \frac{x}{x + 1}) (x + 1)^{2 x}

What is the derivative of (x+1^{2x}) ?
The derivative of (x+1^{2x}) is 2(ln(x+1)+x/(x+1))(x+1)^{2x}
What is the first derivative of (x+1^{2x}) ?
The first derivative of (x+1^{2x}) is 2(ln(x+1)+x/(x+1))(x+1)^{2x}