What is the derivative of (1+x^{3x}) ?

The derivative of (1+x^{3x}) is 3(ln(1+x)+x/(1+x))(1+x)^{3x}

What is the first derivative of (1+x^{3x}) ?

The first derivative of (1+x^{3x}) is 3(ln(1+x)+x/(1+x))(1+x)^{3x}

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 + x)^{3 x})

3 (ln (1 + x) + \frac{x}{1 + x}) (1 + x)^{3 x}

Solution steps

\frac{d}{d x} ((1 + x)^{3 x})

Apply exponent rule:

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

(1 + x)^{3 x} = e^{3 x l n (1 + x)}

= \frac{d}{d x} (e^{3 x l n (1 + x)})

Apply the chain rule:

e^{3 x l n (1 + x)} \frac{d}{d x} (3 x ln (1 + x))

= e^{3 x l n (1 + x)} \frac{d}{d x} (3 x ln (1 + x))

\frac{d}{d x} (3 x ln (1 + x)) = 3 (ln (1 + x) + \frac{x}{1 + x})

= e^{3 x l n (1 + x)} \cdot 3 (ln (1 + x) + \frac{x}{1 + x})

e^{3 x l n (1 + x)} = (1 + x)^{3 x}

= 3 (ln (1 + x) + \frac{x}{1 + x}) (1 + x)^{3 x}

x y^{^{'}} + y = 25 x

d y - (y - 4)^{2} d x = 0

\frac{d}{d x} (cos^{2} (x s i) n^{2} x)

\frac{\partial}{\partial x} (x arcsin (x y))

f (x) = \frac{6}{x}

What is the derivative of (1+x^{3x}) ?
The derivative of (1+x^{3x}) is 3(ln(1+x)+x/(1+x))(1+x)^{3x}
What is the first derivative of (1+x^{3x}) ?
The first derivative of (1+x^{3x}) is 3(ln(1+x)+x/(1+x))(1+x)^{3x}