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Let me try latex for the first time...

[tex]\frac {dy} {dx} \frac {\sin(x)\sec(x)} {1+x\tan(x)} = ?[/tex]

I know the answer is (because of the textbook)

[tex]\frac {1} {(1+x\tan(x))^2}[/tex]

But I came out with a huge answer and i'm stumped. I tried using the product rule for the numerator and then using the quotient rule on the result and the denominator. Keep in mind, we just did those two before doing derivatives of trig functions.