Find the derivative of the function.

Question

f(x) = e^{tan(2x) + sec(2x)}

Answer 1

y=e^tan2x+sec2x

^y'=e^tan2x+sec2x(2sec²2x+2sec2xtan2x)

y'=e^tan2x+sec2x *2sec2x(sec2x+tan2x)

Answer 2

y = exp( tan(2x)+ sec(2x))

y' = exp( tan(2x)+ 2sec(2x)) [ sec^2(2x) + sec(2x)tan(2x)]

Answer 3

This is best handled with a natural log derivative.

First take the ln of both sides:

ln(y)= tan(2x) + sec(2x)

Now take an implicit derivative: [I subbed y for f(x)]

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

[Note that you need to multiply by y' wherever you take the derivative of a y function]

Now you solve algebraically for y':

y' = y* [2*sec^2(2x) + 2*tan(2x)*sec(2x)]

Since y = e^(tan(2x)+sec(2x)) be sure to sub that back in for your final answer.