What is the derivative of arcsec(2x) ?

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

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

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

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

\frac{1}{x 4 x ^{2} - 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

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

Simplify

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

= \frac{1}{x 4 x ^{2} - 1}

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