Calc help, please and thank you :)

I'm not sure what I'm doing wrong, but the site I'm on tells me that it isn't correct.
For f(x)=csc(x) + 5 sec(x) find f '(x)
I got -cscxcotx + 5secxtanx
How is this not correct?
Also
for f(x) = (tanx - 4)/secx how is ((secx)^3-tanxsecx-(tanx)^2+4secx+4tanx)… not correct for the derivative?
Thanks

You are correct on the first part. That is the correct derivative, site must have made an error.

For the 2nd part though:
if y = (tanx - 4)/secx we can rewrite this as tanx/secx - 4/secx.. We can then rewrite that into tanxcosx - 4cosx (since cos = 1/sec and visa versa).. Tanxcosx = sinx.. so You're left with sinx - 4cos x

f(x) sinx - 4cosx--> f'(x) = cosx + 4sinx

d/dx [csc x] = -csc x cot x

and

d/dx[sec x] = sec x tan x

So you are right for the first question.

The function f(x) = (tanx - 4)/secx can be rewritten as

f(x) = (tan(x) - 4) * cos(x)

Try the product rule on that and see if you get a different answer (or an answer that the computer likes)