f(x)=sin(1/x)
f'(x)=cos(1/x)*(1/x)'
=cos(1/x)*x^(-1)
=cos(1/x)*(-1)*x^(-2)
=-cos(1/x)/x²
f(x)=(e^x-1)/x
f'(x)=[(e^x-1)'*x-(e^x-1)*x']/x²
=[x*e^x-(e^x-1)]/x²
=(x*e^x-e^x+1)/x²