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

1 Answer
Jun 9, 2016

Answer:

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

Explanation:

# d/dx [ sec ( - e^(sqrt(x))) ] #

# sec ( e^ (sqrt(x))) * tan ( e^ (sqrt(x))) * d/dx [ ( e^ (sqrt(x))) ] #

# sec ( e^ (sqrt(x))) * tan ( e^ (sqrt(x))) * e^ (sqrt(x)) * d/dx[ sqrt(x) ] #

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

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