Essential Mathematics Formulas: Vectors, Inverse Trigonometric, and Hyperbolic Functions

LIST OF FORMULAS




1. AB = x 2 + y 2 + z 2 16.
d
( cosec−1w ) = −
1 dw
dx w w − 1 dx
2




AB 1  x
2. AB =
AB
17.  a −x2
dx = sin −1   + C
2
a


3.  = cos −1
ab 1 1 x
a b
18. a 2
+x 2
dx = tan −1   + C
a a

nv 1 1  x
4.  = sin −1
n v
19. x x2 − a2
dx =
a
sec−1   + C
a


5. r = a + tv 20. sinh x =
2
(e − e )
1 x −x


ab
6. n =
ab
21. cosh x =
2
(e + e )
1 x −x



1 d dw
7. Area Triangle : AB  AC 22. ( sinh w) = ( cosh w)
2 dx dx

d dv du d dw
8. ( uv ) = u + v 23. ( cosh w) = ( sinh w)
dx dx dx dx dx

du dv
−u v
d u dx dx 24. cosh 2 x = 2cosh 2 x −1
9.  =
dx  v  v 2




d
10. ( tan x ) = sec2 x 25. cosh 2 x = 1 + 2sinh 2 x
dx


11.
d
( sin −1 w ) =
1 dw
26.
d
( cosech w) = ( −cosech w coth w)
dw
dx 1 − w dx
2
dx dx


12.
d
( cos −1 w ) = −
1 dw
27.
d
( tanh w) = ( sech 2 w)
dw
dx 1 − w dx
2
dx dx