y=cot(x/2)^(1/2)求导

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y=cot(x/2)^(1/2)求导
y=cot(x/2)^(1/2)求导

y=cot(x/2)^(1/2)求导
y=cot(x/2)^(1/2)
y’=1/[2√cot(x/2)] ·-csc²(x/2)·1/2
=-1/[4√cot(x/2)] ·csc²(x/2)
=-1/[4sin²(x/2)√cot(x/2)]

(2k*pi,2k*pi+pi] k为整数
首先u>=0
u=cotv>=0的条件是k*pi即k*pi

解:
y'=[cost(x/2)^(1/2)]'[cot(x/2)]'[x/2]'
=1/2[cot(x/2)]^(-1/2)[-csc^2(x/2)][1/2]