y=sin^2(x/3)cot(x/2) 求导

1个回答

y'=[sin²(x/3)]'cot(x/2)+sin²(x/3)[cot(x/2)]'
=2sin(x/3)[sin(x/3)]'*cot(x/2)+sin²(x/3)[-csc²(x/2)]*(x/2)'
=2sin(x/3)cos(x/3)*(x/3)'*cot(x/2)+sin²(x/3)[-csc²(x/2)]*(1/2)
=2sin(x/3)cos(x/3)*(1/3)*cot(x/2)+sin²(x/3)[-csc²(x/2)]*(1/2)
=(1/3)sin(2x/3)*cot(x/2)-(1/2)sin²(x/3)csc²(x/2)

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