How do you differentiate #f(x)=sqrtsec(e^(x) ) # using the chain rule?

1 Answer
Jun 28, 2016

Answer:

#= 1/2 e^x sqrt( sec e^x ) * tan e^x #

Explanation:

#(sqrtsec(e^(x) ))^prime#

using the chain rule and doing it bit by bit....

#= 1/2 1/(sqrt (sec e^x )) * ( sec e^x )^prime #

#= 1/2 1/(sqrt (sec e^x )) * sec e^x tan e^x * (e^x)^prime #

#= 1/2 1/(sqrt (sec e^x )) * sec e^x tan e^x * e^x #

#= 1/2 e^x sqrt( sec e^x ) * tan e^x #