What is the derivative of arcsec(5x) ?

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

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

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

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derivative of

arcsec (5 x)

\frac{1}{x ^{2} 25 x ^{2} - 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x ^{2} 25 x ^{2} - 1}

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