What is the derivative of arccosh(sec(x)) ?

The derivative of arccosh(sec(x)) is (sec(x)tan(x))/(sqrt(sec(x)-1)\sqrt{sec(x)+1)}

What is the first derivative of arccosh(sec(x)) ?

The first derivative of arccosh(sec(x)) is (sec(x)tan(x))/(sqrt(sec(x)-1)\sqrt{sec(x)+1)}

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\frac{d}{d x} (arccosh (sec (x)))

\frac{sec ( x ) tan ( x )}{sec ( x ) - 1 sec ( x ) + 1}

Solution steps

\frac{d}{d x} (arccosh (sec (x)))

Apply the chain rule:

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

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

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= \frac{1}{sec ( x ) - 1 sec ( x ) + 1} sec (x) tan (x)

Simplify

\frac{1}{sec ( x ) - 1 sec ( x ) + 1} sec (x) tan (x) : \frac{sec ( x ) tan ( x )}{sec ( x ) - 1 sec ( x ) + 1}

= \frac{sec ( x ) tan ( x )}{sec ( x ) - 1 sec ( x ) + 1}

What is the derivative of arccosh(sec(x)) ?
The derivative of arccosh(sec(x)) is (sec(x)tan(x))/(sqrt(sec(x)-1)\sqrt{sec(x)+1)}
What is the first derivative of arccosh(sec(x)) ?
The first derivative of arccosh(sec(x)) is (sec(x)tan(x))/(sqrt(sec(x)-1)\sqrt{sec(x)+1)}