y=tan(x+y)的二阶导数
回答
爱扬教育
2022-06-25
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y=-2csc(x+y)*[-csc(x+y)cot(x+y)]*(x+y)
=2csc(x+y)cot(x+y)*(1+y)
=-2csc(x+y)cot(x+y)*[cot(x+y)]
=-2csc(x+y)cot(x+y)
扩展资料
y=tan(x+y)
y'=sec(x+y)*(x+y)'
=sec(x+y)*(1+y')
=sec(x+y)+y'sec(x+y)
y'-y'sec(x+y)=sec(x+y)
y'=sec(x+y)/[1-sec(x+y)]
=sec(x+y)/{-[sec(x+y)-1]}
=sec(x+y)/[-tan(x+y)]
=-1/cos(x+y)*cos(x+y)/sin(x+y)
=-csc(x+y)