What is the derivative of arcsec(5ln(2x)) ?

The derivative of arcsec(5ln(2x)) is 1/(xsqrt(ln^2(2x))\sqrt{25ln^2(2x)-1)}

What is the first derivative of arcsec(5ln(2x)) ?

The first derivative of arcsec(5ln(2x)) is 1/(xsqrt(ln^2(2x))\sqrt{25ln^2(2x)-1)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative

\frac{1}{x ln ^{2} ( 2 x ) 25 ln ^{2} ( 2 x ) - 1}

Solution steps

\frac{d}{d x} (arcsec (5 ln (2 x)))

Apply the chain rule:

\frac{1}{( 5 ln ( 2 x ) ) ^{2} ( 5 ln ( 2 x ) ) ^{2} - 1} \frac{d}{d x} (5 ln (2 x))

= \frac{1}{( 5 ln ( 2 x ) ) ^{2} ( 5 ln ( 2 x ) ) ^{2} - 1} \frac{d}{d x} (5 ln (2 x))

\frac{d}{d x} (5 ln (2 x)) = \frac{5}{x}

= \frac{1}{( 5 ln ( 2 x ) ) ^{2} ( 5 ln ( 2 x ) ) ^{2} - 1} \cdot \frac{5}{x}

Simplify

\frac{1}{( 5 ln ( 2 x ) ) ^{2} ( 5 ln ( 2 x ) ) ^{2} - 1} \cdot \frac{5}{x} : \frac{1}{x ln ^{2} ( 2 x ) 25 ln ^{2} ( 2 x ) - 1}

= \frac{1}{x ln ^{2} ( 2 x ) 25 ln ^{2} ( 2 x ) - 1}

What is the derivative of arcsec(5ln(2x)) ?
The derivative of arcsec(5ln(2x)) is 1/(xsqrt(ln^2(2x))\sqrt{25ln^2(2x)-1)}
What is the first derivative of arcsec(5ln(2x)) ?
The first derivative of arcsec(5ln(2x)) is 1/(xsqrt(ln^2(2x))\sqrt{25ln^2(2x)-1)}