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