What is the derivative of h(x)=arcsec(2x) ?

The derivative of h(x)=arcsec(2x) is 1/(sqrt(x^2)\sqrt{4x^2-1)}

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

The first derivative of h(x)=arcsec(2x) is 1/(sqrt(x^2)\sqrt{4x^2-1)}

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derivative of

h (x) = arcsec (2 x)

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

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

What is the derivative of h(x)=arcsec(2x) ?
The derivative of h(x)=arcsec(2x) is 1/(sqrt(x^2)\sqrt{4x^2-1)}
What is the first derivative of h(x)=arcsec(2x) ?
The first derivative of h(x)=arcsec(2x) is 1/(sqrt(x^2)\sqrt{4x^2-1)}