Page 46 - Aeronautical Engineer Data Book

Fundamental dimensions and units 33

d d u
u
u
3
3 3 a = a ln a 3
d x dx
d 1 d u
3 3 log a u = log a e 3 3 3
3
d x u dx
Derivatives of trigonometric functions in
radians
d d
3 3 sin x = cos x, 3 3 cos x = – sin x
d x d x
d
2
2
3 3 tan x = sec x = 1 + tan x
d x
d
2
3 3 cot x = –cosec x
d x
d sin x
3 3 sec x = 3 3 = sec x tan x
d x c os 2 x
d cos x
3 3 cosec x = – 3 3 = – cosec x cot x
d x s in 2 x
d d
3
3 3 arcsin x = – 3 arccos x
d x d x
1
= 33 for angles in the
(1 – x 2 1/2
)
first quadrant.
Derivatives of hyperbolic functions
d d
3 3 sinh x = cosh x, 3 3 cosh x = sinh x
d x d x
d d
2
2
3 3 tanh x = sech x, 3 3 cosh x = – cosech x
d x d x
d 1
3 3 (arcsinh x) = 3 3,
d x (x 2 +1) 1/2
d ±1
3 3 (arccosh x) = 3 3
2
d x (x –
1) 1/2