What is the derivative of arcsec(2^x) ?

The derivative of arcsec(2^x) is (ln(2))/(sqrt(4^x-1))

What is the first derivative of arcsec(2^x) ?

The first derivative of arcsec(2^x) is (ln(2))/(sqrt(4^x-1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{ln ( 2 )}{4 ^{x} - 1}

Solution steps

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

Apply the chain rule:

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

= \frac{1}{( 2 ^{x} ) ^{2} ( 2 ^{x} ) ^{2} - 1} \frac{d}{d x} (2^{x})

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

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

Simplify

\frac{1}{( 2 ^{x} ) ^{2} ( 2 ^{x} ) ^{2} - 1} \cdot 2^{x} ln (2) : \frac{ln ( 2 )}{4 ^{x} - 1}

= \frac{ln ( 2 )}{4 ^{x} - 1}

What is the derivative of arcsec(2^x) ?
The derivative of arcsec(2^x) is (ln(2))/(sqrt(4^x-1))
What is the first derivative of arcsec(2^x) ?
The first derivative of arcsec(2^x) is (ln(2))/(sqrt(4^x-1))