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>0 and a are not equal to 1, x >；; 0)
f(x)=lnx
f'(x)= 1/x
(x & gt0)
f(x)=tanx
f'(x)= 1/cos^2
x
f(x)=cotx
f'(x)=-
1/sin^2
x
The derivative algorithm is as follows
(f(x)+/-g(x))'=f'(x)+/-
g'(x)
(f(x)g(x))'=f'(x)g(x)+f(x)g'(x)
(g(x)/f(x))'=(f(x)'g(x)-g(x)f'(x))/(f(x))^2