standard formulae for nth derivatives:
- D n (e ax) = a n e ax
- D n (a mx ) = (m log a ) n a mx
- D n (ax+b ) m= m (m-1)(m-2) ..........[m-(n-1)] (ax+b) m-n a n
- D n [1/ (ax+b)]= [(-1) n n! (n-1)!]/ [(ax+b) n+1]
- D n [log (ax+b)] =[a n (-1) n-1 (n-1)!]/[(ax+b) n]
- D n [sin(ax+b)] = a n [sin(n pie/2+ax+b)]
- D n [cos(ax+b)] = a n [cos(n pie/2+ax+b)]
- D n [e ax .sin(bx+c)]= [(a 2 +b 2 ) 1/2 ] n e ax [sin{n tan -1 (b/a)+ (bx+c)}]
- D n [e ax .cos (bx+c)] = [(a 2 +b 2 )1/2 ] n e ax [cos{n tan -1 (b/a)+(bx+c)}]
- D n (x n ) = n!
- D n (x m )= m! x m-n/(m-n)!
- D n (e x )= e x
- D n [1/(x 2 + b 2 )] = {(-1) n n! sin n+1 A sin (n+1)A}/{b n+2} (where A=tan -1 (a/x))
- D n [tan -1 x]= (-1) n-1 (n-1)! sin n A sin n A [where A=cot -1 x]
