What is the derivative of arcsec(2x+1) ?

The derivative of arcsec(2x+1) is 1/((2x+1)sqrt(x(x+1)))

What is the first derivative of arcsec(2x+1) ?

The first derivative of arcsec(2x+1) is 1/((2x+1)sqrt(x(x+1)))

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\frac{d}{d x} (arcsec (2 x + 1))

\frac{1}{( 2 x + 1 ) x ( x + 1 )}

Solution steps

\frac{d}{d x} (arcsec (2 x + 1))

Apply the chain rule:

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

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

\frac{d}{d x} (2 x + 1) = 2

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

Simplify

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

= \frac{1}{( 2 x + 1 ) x ( x + 1 )}

What is the derivative of arcsec(2x+1) ?
The derivative of arcsec(2x+1) is 1/((2x+1)sqrt(x(x+1)))
What is the first derivative of arcsec(2x+1) ?
The first derivative of arcsec(2x+1) is 1/((2x+1)sqrt(x(x+1)))