f(x)=c f'(x)=0
f(x)=x^a f'(x)=ax^(a-1)
f(x)=sin x f'(x)=cos x
f(x)=cos x f'(x)=-sin x
f(x)=a^x f'(x)=(a^x)lna
f(x)=e^x f'(x)=e^x
f(x)=logax f"(x)=1/(xlnx)
f(x)=lnx f'(x)=1/x