Question

find the second derivative of f(x)=cosx+3secx
help pls

Answer 1

would the first drivative be -sinx+3tanxsecx?

Answer 2

you are correct

Answer 3

derive that to get f '' (x)

you'll have to use the product rule to derive tan(x)*sec(x)

Answer 4

would the 2nd deri be -cosx+3secx^2secs+3tanxtanxsecx?

Answer 5

correct, you can do a bit of simplification but you have the correct answer more or less

Answer 6

how do you simplify that?

Answer 7

well you could factor out 3sec(x) from 3secx^2secx+3tanxtanxsecx to get

3sec(x)*[sec^2(x) + tan^2(x)]

Answer 8

so overall, the second derivative is

f '' (x) = -cos(x) + 3sec(x)*[sec^2(x) + tan^2(x)]

Answer 9

hmmm ok thanks :D

Answer 10

you're welcome