Fórmulasdederivaciónparafuncionesalgebraicas

𝑑𝑑𝑦 𝑐 = 0

𝑑𝑑𝑦 𝑥 = 1

𝑑𝑑𝑦 𝑥

! = 𝑛𝑥!!!

𝑑𝑑𝑦 𝑢

! = 𝑛𝑢!!!𝑑𝑑𝑥 𝑢

𝑑𝑑𝑦 𝑢 + 𝑣 − 𝑤 =

𝑑𝑑𝑦 𝑢 +

𝑑𝑑𝑦 𝑣 −

𝑑𝑑𝑦𝑤

𝑑𝑑𝑥 𝑢𝑣 = 𝑢

𝑑𝑑𝑦 𝑣 + 𝑣

𝑑𝑑𝑦 𝑢

𝑑𝑑𝑥

𝑢𝑣 =

𝑣 𝑑𝑑𝑦 𝑢 − 𝑢

𝑑𝑑𝑦 𝑣

𝑣!

𝑑𝑑𝑥

𝑢𝑐 =

1𝑐

𝑑𝑑𝑥 𝑢

𝑑𝑑𝑥

𝑐𝑢 = −

𝑐𝑢!

𝑑𝑑𝑥 𝑢

𝑑𝑑𝑥 𝑢! =

𝑑𝑑𝑥 𝑢

𝑛𝑢!!!!

𝑑𝑑𝑦 𝑢

! = 𝑣 ∙ 𝑢!!!𝑑𝑑𝑥 𝑢 + 𝑙𝑛 𝑢 ∙ 𝑢!

𝑑𝑑𝑥 𝑣

Si𝑦 = 𝑓 𝑢 y𝑢 = 𝑔 𝑥 ,entonces𝑦 = 𝑓 𝑔 ! ,suderivadaseobtienemediantelaRegladelaCadena

𝑑𝑦𝑑𝑥 =

𝑑𝑦𝑑𝑢 ∙

𝑑𝑢𝑑𝑥

ó

𝑑𝑑𝑥 𝑓 𝑔 ! = 𝑓′ 𝑔 ! ∙ 𝑔′ !

Fórmulasdederivaciónparafuncionestrascendentes

𝑑𝑑𝑥 𝑙𝑛𝑣 =

1𝑣𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑙𝑜𝑔!𝑣 =

𝑙𝑜𝑔!𝑒𝑣

𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑒

! = 𝑒!𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑎

! = 𝑎!𝑙𝑛𝑎𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑠𝑒𝑛𝑣 = 𝑐𝑜𝑠𝑣

𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑐𝑜𝑠𝑣 = −𝑠𝑒𝑛𝑣

𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑡𝑎𝑛𝑣 = 𝑠𝑒𝑐!𝑣

𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑐𝑜𝑡𝑣 = −𝑐𝑠𝑐!𝑣

𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑠𝑒𝑐𝑣 = 𝑠𝑒𝑐𝑣 ∙ 𝑡𝑎𝑛𝑣

𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑐𝑠𝑐𝑣 = −𝑐𝑠𝑐𝑣 ∙ 𝑐𝑜𝑡𝑣

𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑎𝑟𝑐𝑠𝑒𝑛𝑣 =

11− 𝑣!

𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑎𝑟𝑐𝑐𝑜𝑠𝑣 = −

11− 𝑣!

𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑎𝑟𝑐𝑡𝑎𝑛𝑣 =

11+ 𝑣!

𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑎𝑟𝑐𝑐𝑜𝑡𝑣 = −

11+ 𝑣!

𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑎𝑟𝑐𝑠𝑒𝑐𝑣 =

1𝑣 𝑣! − 1

𝑑𝑑𝑥 𝑣

𝑑𝑑𝑥 𝑎𝑟𝑐𝑠𝑒𝑐𝑣 = −

1𝑣 𝑣! − 1

𝑑𝑑𝑥 𝑣