What is the derivative of sec(x/2) ?

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

What is the first derivative of sec(x/2) ?

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

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\frac{d}{d x} (sec (\frac{x}{2}))

sec (\frac{x}{2}) tan (\frac{x}{2}) \frac{1}{2}

Solution steps

\frac{d}{d x} (sec (\frac{x}{2}))

Apply the chain rule:

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

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

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

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

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