en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 2^{3^x}

Solution

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

Solution

ln (2) ln (3) \cdot 3^{x} \cdot 2^{3^{x}}

Solution steps

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

Apply exponent rule:

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

2^{3^{x}} = e^{3^{x} l n (2)}

= \frac{d}{d x} (e^{3^{x} l n (2)})

Apply the chain rule:

e^{3^{x} l n (2)} \frac{d}{d x} (3^{x} ln (2))

= e^{3^{x} l n (2)} \frac{d}{d x} (3^{x} ln (2))

\frac{d}{d x} (3^{x} ln (2)) = ln (2) \cdot 3^{x} ln (3)

= e^{3^{x} l n (2)} ln (2) \cdot 3^{x} ln (3)

e^{3^{x} l n (2)} = 2^{3^{x}}

= ln (2) ln (3) \cdot 3^{x} \cdot 2^{3^{x}}

Popular Examples

limit as x approaches 1 of (2x)/(x^2-1)

x \to 1 lim (\frac{2 x}{x ^{2} - 1})

derivative of arctan(2t)derivative of

arctan (2 t)

derivative of ln(24x)

\frac{d}{d x} (ln (24 x))

integral of cos^2(2x)

\int cos^{2} (2 x) d x

integral from 3 to infinity of 5/(x^2-x)

\int_{3}^{\infty} \frac{5}{x ^{2} - x} d x

Frequently Asked Questions (FAQ)

What is the derivative of 2^{3^x} ?
The derivative of 2^{3^x} is ln(2)ln(3)*3^x*2^{3^x}
What is the first derivative of 2^{3^x} ?
The first derivative of 2^{3^x} is ln(2)ln(3)*3^x*2^{3^x}