2 trigonometric calculus Q.

1) dy/dx = x d(√sin x)/dx + √sin x

= [x/(2√sin x)] d(sin x)/dx + √sin x

= [x cos x/(2√sin x)] + √sin x

= (x cos x + 2 sin x)/(2√sin x)

2) dy/dx = sec2 x d(csc x)/dx + csc x d(sec2 x)/dx

= - sec2 x csc x cot x + 2 csc x sec x d(sec x)/dx

= - sec2 x csc x cot x + 2 csc x sec2 x tan x

= sec2 x csc x (2 tan x - cot x)

2011-08-15 23:38:51 補充：
2) Multiplying sec x csc x into the bracket:

sec x ( 2 tan x sec x csc x - cot x csc x sec x)
= sec x ( 2 sec^2 x - csc^2 x)