Calculus
posted by gnozahs .
find the derivative of f(x)=tanx4/secx
I used the quotient rule and got (sec^2x4)(secx)(tanx4)(cosx)/sec^2x but I'm pretty sure that's wrong. Help. Thanks.

It is not clear what your expression really is, there are two possibilities. In both cases, it pays to do a little simplification before differentiating.
If f(x)=(tan(x)4)/sec(x)
then
f(x)
=tan(x)*cos(x)  4 cos(x)
=sin(x)  4 cos(x)
f'(x) = cos(x) + 4 sin(x)
If f(x) = tan(x)  4/sec(x)
then
f(x) = tan(x)  4 cos(x)
f'(x) = sec^{2}(x) + 4 sin(x) 
cos(x) + 4 sin(x) is correct. How did the 4 end up with the sin and not with the cos?

It comes from
4/sec(x) = 4 cos(x)
So when differentiated, it gives 4 sin(x)