What is the derivative of sqrt(1/(cos(x))) ?

The derivative of sqrt(1/(cos(x))) is (sec(x)tan(x)sqrt(cos(x)))/2

What is the first derivative of sqrt(1/(cos(x))) ?

The first derivative of sqrt(1/(cos(x))) is (sec(x)tan(x)sqrt(cos(x)))/2

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derivative of

\frac{1}{cos ( x )}

\frac{sec ( x ) tan ( x ) cos ( x )}{2}

Solution steps

\frac{d}{d x} (\frac{1}{cos ( x )})

Apply the chain rule:

\frac{1}{2 \frac{1}{c o s ( x )}} \frac{d}{d x} (\frac{1}{cos ( x )})

= \frac{1}{2 \frac{1}{c o s ( x )}} \frac{d}{d x} (\frac{1}{cos ( x )})

\frac{d}{d x} (\frac{1}{cos ( x )}) = sec (x) tan (x)

= \frac{1}{2 \frac{1}{c o s ( x )}} sec (x) tan (x)

Simplify

\frac{1}{2 \frac{1}{c o s ( x )}} sec (x) tan (x) : \frac{sec ( x ) tan ( x ) cos ( x )}{2}

= \frac{sec ( x ) tan ( x ) cos ( x )}{2}

What is the derivative of sqrt(1/(cos(x))) ?
The derivative of sqrt(1/(cos(x))) is (sec(x)tan(x)sqrt(cos(x)))/2
What is the first derivative of sqrt(1/(cos(x))) ?
The first derivative of sqrt(1/(cos(x))) is (sec(x)tan(x)sqrt(cos(x)))/2