基本函式的導函式
C'=0(C為常數)
(x^n)'=nx^(n-1) (n∈R)
(sinx)'=cosx
(cosx)'=-sinx
(e^x)'=e^x
(a^x)'=(a^x)*lna(a>0且a≠1)
[logax)]' = 1/x*(logae)(a>0且a≠1)
[lnx]'= 1/x
和差積商函式的導函式
[f(x) + g(x)]' = f'(x) + g'(x)
[f(x) - g(x)]' = f'(x) - g'(x)
[f(x)g(x)]' = f'(x)g(x) + f(x)g'(x)
[f(x)/g(x)]' = [f'(x)g(x) - f(x)g'(x)] / [g(x)^2]
複合函式的導函式
設 y=u(t) ,t=v(x),則 y'(x) = u'(t)v'(x) = u'[v(x)] v'(x)
例 :y = t^2 ,t = sinx ,則y'(x) = 2t * cosx = 2sinx*cosx = sin2x
基本函式的導函式
C'=0(C為常數)
(x^n)'=nx^(n-1) (n∈R)
(sinx)'=cosx
(cosx)'=-sinx
(e^x)'=e^x
(a^x)'=(a^x)*lna(a>0且a≠1)
[logax)]' = 1/x*(logae)(a>0且a≠1)
[lnx]'= 1/x
和差積商函式的導函式
[f(x) + g(x)]' = f'(x) + g'(x)
[f(x) - g(x)]' = f'(x) - g'(x)
[f(x)g(x)]' = f'(x)g(x) + f(x)g'(x)
[f(x)/g(x)]' = [f'(x)g(x) - f(x)g'(x)] / [g(x)^2]
複合函式的導函式
設 y=u(t) ,t=v(x),則 y'(x) = u'(t)v'(x) = u'[v(x)] v'(x)
例 :y = t^2 ,t = sinx ,則y'(x) = 2t * cosx = 2sinx*cosx = sin2x