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Popular >

derivative of 1/(cos(x/2))

Solution

derivative of

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

Solution

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

Solution steps

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

Simplify

\frac{1}{cos ( \frac{x}{2} )} : sec (\frac{x}{2})

= \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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Frequently Asked Questions (FAQ)

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