Y=f(x)=c (c is a constant), then f'(x)=0.
F (x) = x n (n is not equal to 0) f' (x) = NX (n- 1) (x n stands for the n power of x).
f(x)=sinx f'(x)=cosx
f(x)=cosx f'(x)=-sinx
f(x)=a^x f'(x)=a^xlna(a>； 0 and a are not equal to 1, x >；; 0)
f(x)=e^x f'(x)=e^x
f(x)= logaX f '(x)= 1/xlna(a & gt； 0 and a are not equal to 1, x >；; 0)
f(x)= lnx f '(x)= 1/x(x & gt； 0)
f(x)=tanx f'(x)= 1/cos^2 x
f(x)=cotx f'(x)=- 1/sin^2 x
If the derivative is positive, it will increase monotonically in this interval, and if it is negative, it will decrease monotonically.