Formulario calculo diferencial

FORMULARIO DE DERIVADAS.

TRIGONOMÉTRICAS 9) 𝑦 = 𝑠𝑒𝑛(𝑢) 𝑦 = 𝑢𝑐𝑜𝑠(𝑢) 1) 𝑦 = 𝑐

BÁSICAS 𝑦 = 0; 𝑐 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑒

10) 𝑦 = 𝑐𝑜𝑠(𝑢)

𝑦 = −𝑢𝑠𝑒𝑛(𝑢)

2) 𝑦 = 𝑥

𝑦 = 1

11)𝑦 = 𝑡𝑎𝑛(𝑢)

𝑦 = 𝑢𝑠𝑒𝑐 2 (𝑢)

3) 𝑦 = 𝑐𝑣

𝑦 = 𝑐𝑣

12) 𝑦 = 𝑐𝑜𝑡(𝑢)

𝑦 = −𝑢𝑐𝑠𝑐 2 (𝑢)

4) 𝑦 = 𝑥 𝑛

𝑦 = 𝑛𝑥 𝑛−1

13)𝑦 = 𝑠𝑒𝑐(𝑢)

𝑦 = 𝑢𝑠𝑒𝑐(𝑢 )𝑡𝑎𝑛(𝑢)

4𝑎) 𝑦 = 𝑐𝑥 𝑛

𝑦 = 𝑐𝑛𝑥 𝑛−1 . 𝑣

14) 𝑦 = 𝑐𝑠𝑐(𝑢)

𝑦 = −𝑢𝑐𝑠𝑐(𝑢) 𝑐𝑜𝑡(𝑢)

5) 𝑦 = 𝑢 + 𝑣 − 𝑤

𝑦 = 𝑢 + 𝑣 − 𝑤

6) 𝑦 = 𝑢. 𝑣

𝑦 = 𝑢𝑣 + 𝑣𝑢

TRIGONOMÉTRICAS INVERSAS 𝑢 15)𝑦 = 𝑎𝑟𝑐 𝑠𝑒𝑛(𝑢) 𝑦 = √1 − 𝑢2 𝑢 16) 𝑦 = 𝑎𝑟𝑐 𝑐𝑜𝑠(𝑢) 𝑦 = − √1 − 𝑢2 𝑢 17)𝑦 = 𝑎𝑟𝑐 𝑡𝑎𝑛(𝑢) 𝑦 = 1 + 𝑢2 𝑢 18) 𝑦 = 𝑎𝑟𝑐 𝑐𝑜𝑡(𝑢) 𝑦 = − 1 + 𝑢2 𝑢 19)𝑦 = 𝑎𝑟𝑐 𝑠𝑒𝑐(𝑢) 𝑦 = 𝑢√𝑢2 − 1 𝑢 20)𝑦 = 𝑎𝑟𝑐 𝑐𝑠𝑐(𝑢) 𝑦 = − 𝑢√𝑢2 − 1 EXPONENCIALES 𝑢 23)𝑦 = 𝑒 𝑦 = 𝑢𝑒 𝑢

7) 𝑦 =

𝑢 𝑣

8) 𝑦 = √𝑢

𝑦 =

𝑦 =

𝑣𝑢 − 𝑢𝑣 𝑣2 𝑢 2√𝑢

LOGARÍTMICAS 𝑢 21)𝑦 = 𝑙𝑛(𝑢) 𝑦 = 𝑢 𝑢 22)𝑦 = 𝑙𝑜𝑔𝑎 (𝑢) 𝑦 = 𝑢𝑙𝑛(𝑎) PROPIEDADES DE LOS EXPONENTES 1 𝑎0 = 1 = 𝑎−𝑛 𝑎1 = 𝑎 𝑎𝑛 1 𝑎𝑚 𝑎𝑛 = 𝑎𝑛+𝑚 𝑎𝑛 = −𝑛 𝑛 𝑛 𝑛 𝑎 𝑏 = (𝑎𝑏) 𝑎 𝑎𝑚 𝑎𝑛 𝑎 𝑛 𝑆𝑖 𝑚 > 𝑛; 𝑛 = 𝑎𝑚−𝑛 =( ) 𝑛 𝑎𝑚 𝑏 𝑏 𝑚 𝑛 𝑚𝑛 𝑎 (𝑎 ) = 𝑎 𝑆𝑖 𝑚 = 𝑛; 𝑛 = 𝑎0 = 1 𝑎𝑚 𝑎 1 𝑆𝑖 𝑚 < 𝑛; 𝑛 = 𝑛−𝑚 𝑎 𝑎

24) 𝑦 = 𝑎𝑢

𝑦 = 𝑢𝑎𝑢 𝑙𝑛(𝑎)

PROPIEDADES DE LOS RADICALES 𝑛

𝑛

√𝑎𝑛 = 𝑎𝑛 = 𝑎 𝑚

𝑛

√𝑎𝑚 = 𝑎 𝑛 𝑚

𝑚𝑛

𝑛

𝑛 𝑚 √𝑎 = √ √𝑎 = √ √𝑎 𝑛

𝑛

𝑛

√𝑎 √𝑏 = √𝑎𝑏 𝑛 𝑛 𝑎 √𝑎 √ =𝑛 𝑏 √𝑏