Find the second derivative of `y = e^(tan 2x)`

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justaguide eNotes educator| Certified Educator

The second derivative of `y = e^(tan 2x)` has to be found. This is done using the chain rule and the product rule.

y' = `2*sec^2(2x)*e^(tan 2x)`

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

= `8*sec^2(2x)*tan 2x*e^(tan 2x) + 4*sec^4(2x)*e^(tan 2x)`

The required second derivative is `8*sec^2(2x)*tan 2x*e^(tan 2x) + 4*sec^4(2x)*e^(tan 2x)`

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