Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises - Page 123: 54

$ f(x)=g(x)=x $ $ f'(x)=g'(x)=\frac{d}{dx}(x)=1$ $(\frac{f}{g})'=\frac{f'g-fg'}{g^{2}}=\frac{1\times x-x\times1}{x^{2}}=0$ $\frac{f'}{g'}=\frac{1}{1}=1$ We see that $(\frac{f}{g})'\ne \frac{f'}{g'}$

See the answer above.