What is the derivative of arcsech(sin(x)) ?

The derivative of arcsech(sin(x)) is -(cot(x))/(sqrt(sin(x)+1)\sqrt{-sin(x)+1)}

What is the first derivative of arcsech(sin(x)) ?

The first derivative of arcsech(sin(x)) is -(cot(x))/(sqrt(sin(x)+1)\sqrt{-sin(x)+1)}

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\frac{d}{d x} (arcsech (sin (x)))

- \frac{cot ( x )}{sin ( x ) + 1 - sin ( x ) + 1}

Solution steps

\frac{d}{d x} (arcsech (sin (x)))

Apply the chain rule:

- \frac{1}{sin ( x ) sin ( x ) + 1 - sin ( x ) + 1} \frac{d}{d x} (sin (x))

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

\frac{d}{d x} (sin (x)) = cos (x)

= - \frac{1}{sin ( x ) sin ( x ) + 1 - sin ( x ) + 1} cos (x)

Simplify

- \frac{1}{sin ( x ) sin ( x ) + 1 - sin ( x ) + 1} cos (x) : - \frac{cot ( x )}{sin ( x ) + 1 - sin ( x ) + 1}

= - \frac{cot ( x )}{sin ( x ) + 1 - sin ( x ) + 1}

What is the derivative of arcsech(sin(x)) ?
The derivative of arcsech(sin(x)) is -(cot(x))/(sqrt(sin(x)+1)\sqrt{-sin(x)+1)}
What is the first derivative of arcsech(sin(x)) ?
The first derivative of arcsech(sin(x)) is -(cot(x))/(sqrt(sin(x)+1)\sqrt{-sin(x)+1)}