Question

find the derivative of f(x)=tanx-4/secx

I used the quotient rule and got (sec^2x-4)(secx)-(tanx-4)(cosx)/sec^2x but I'm pretty sure that's wrong. Help. Thanks.

Answer 1

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) = sec²(x) + 4 sin(x)

Answer 2

cos(x) + 4 sin(x) is correct. How did the 4 end up with the sin and not with the cos?

Answer 3

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