trigo differentiation 兩條only! 急.

Chain rule is a very powerful method to solve the problem.

1. y = 2sin(x/2) - cos3x

Differentiate both sides with respect to x

dy/dx = 2 d[sin(x/2)]/d(x/2) X d(x/2)/dx - d(cos3x)/d(3x) X d(3x)/dx

= 2(1/2)cos(x/2) - 3(-sin3x)

= cos(x/2) + 3sin3x


2. y = cot√x

Differentiate both sides with respect to x

dy/dx = d(cot√x)/d(√x) X d(√x)/dx

= -cosec2√x X 1/2√x

= -cosec2√x / 2√x