13explog.pdf - AF T Differentiation of Exp and Log...

This preview shows page 1 - 7 out of 14 pages.

Differentiation of Exp and Log, l’Hˆopital’s RuleYong LiuDept of Math and StatsAuburn UniversityAuburn, USOct, 2018
Proposition (Derivative of Exp)ddx(ex) =Yong Liu(Auburn University)Differentiation of Exp and Log, l’Hopital’s RuleOct 20182 / 5
Proposition (Derivative of Exp)ddx(ex) =ex.Proof.f0(x)=limh0f(x+h)-f(x)h= limh0ex+h-exh=limh0ex(eh-1)h=exlimh0eh-1h=ex.(Recall the definition ofeh).Yong Liu(Auburn University)Differentiation of Exp and Log, l’Hopital’s RuleOct 20182 / 5
2 / 5
Many examplesExample(1) Find the derivative of (1)f(x) =x2exand (2)g(t) = (et+ 2)3/2.Yong Liu(Auburn University)Differentiation of Exp and Log, l’Hopital’s RuleOct 20183 / 5
Many examplesExample(1) Find the derivative of (1)f(x) =x2exand (2)g(t) = (et+ 2)3/2.

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture