Posted by **gnozahs** on Wednesday, June 10, 2009 at 11:42pm.

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.

- Calculus -
**MathMate**, Wednesday, June 10, 2009 at 11:52pm
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)

- Calculus -
**gnozahs**, Wednesday, June 10, 2009 at 11:58pm
cos(x) + 4 sin(x) is correct. How did the 4 end up with the sin and not with the cos?

- Calculus -
**MathMate**, Thursday, June 11, 2009 at 12:05am
It comes from

-4/sec(x) = -4 cos(x)

So when differentiated, it gives 4 sin(x)

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