I'm having problems understanding \(\displaystyle \frac{dy}{dx}\(\frac{1}{x})\)

I always get 0 when I try to solve it with conventional algebra but the answer is \(\displaystyle \frac{-1}{x^2}\)

Bonus question: How do I get the enclosing brackets in my tex code to cover \(\displaystyle \frac{1}{x}\) completely, instead of being small? Also, how do I do a space between \(\displaystyle \frac{dy}{dx}\) and \(\displaystyle \frac{1}{x}\) ?

Thanks!