Homework Help

Find y' and y" if y = ln(sec 2x + tan 2x)

alisabliny's profile pic

Posted via web

dislike 1 like

Find y' and y" if y = ln(sec 2x + tan 2x)

1 Answer | Add Yours

justaguide's profile pic

Posted (Answer #1)

dislike 2 like

The function `y= ln(sec 2x + tan 2x)`

This can be differentiated using the chain rule.

y' = `(1/(sec 2x + tan 2x))*(2*sec 2x*tan 2x + 2*sec^2 2x)`

=>  `(2*sec 2x*tan 2x + 2*sec^2 2x)/(sec 2x + tan 2x)`

=> `2*sec 2x(tan 2x + sec 2x)/(sec 2x + tan 2x)`

=> `2*sec 2x`

y'' = `2*2*sec 2x*tan 2x`

=> `4*sec 2x*tan 2x`

The derivatives of `y= ln(sec 2x + tan 2x)` are `y' = 2*sec 2x ` and `y''= 4*sec 2x*tan 2x`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes