For the function f(x)=3x\displaystyle {f{{\left({x}\right)}}}=\frac{{3}}{{x}}, apply the definition of the derivative.
Evaluate each of the following and enter your answers in simplest form:

Step 1 f(x+h)=\displaystyle {f{{\left({x}+{h}\right)}}}=  
Step 2 f(x+h)f(x)=\displaystyle {f{{\left({x}+{h}\right)}}}-{f{{\left({x}\right)}}}=  
Step 3 f(x+h)f(x)h=\displaystyle \frac{{{f{{\left({x}+{h}\right)}}}-{f{{\left({x}\right)}}}}}{{h}}=  
Step 4 limh0f(x+h)f(x)h=\displaystyle \lim_{{{h}\to{0}}}\frac{{{f{{\left({x}+{h}\right)}}}-{f{{\left({x}\right)}}}}}{{h}}=  

So, f(x)=\displaystyle {f}'{\left({x}\right)}=