Derivative Formulas 1 - Kennedy PDF

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Derivatives I

 Dx  c   0  , where c is a real constant. Dx  cu( x )   cDx  u (x )   cu  (x ) Dx  u(x )  v (x )   Dx  u (x )  Dx  v (x )   u (x ) v  (x ) Dx  u(x) v (x )  u (x )Dx  v (x )  v (x )Dx  u (x )  u (x )v (x ) v (x )u  (x )

 u (x )  v (x ) Dx  u (x )   u (x )Dx  v (x )  v (x ) u (x )  u (x )v (x ) Dx     v (x )  v (x )2 v (x )2

f

  g  x   f  g ( x)   g ( x)



Dx  u (x )

n

  n u (x ) 

Dx  u( x)   Dy x 

n 1

 u  (x )

u( x )  u ( x ) u( x)

1 Dx y

Dx  sin u(x)   cosu(x)  u (x ) Dx  cosu( x)     sin u( x)  u ( x)

Dx  tan u( x)   sec 2  u (x )  u  (x ) Dx  cot  u( x)    csc 2 u( x)   u ( x)

Dx  sec u( x)   sec u( x) tan u( x)  u  (x ) Dx  csc u( x)     csc u( x) cot u( x)  u ( x)

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