什么求导后=sin^4x
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什么求导后=sin^4x
什么求导后=sin^4x
什么求导后=sin^4x
根据倍角公式cos2x=1-2(sinx)^2=2(cosx)^2-1
((sinx)^2)^2
=(1-cos2x)^2/4
=1/4+[(cos2x)^2]/4-1/2cos2x
=1/4+(1+cos4x)/8-1/2cos2x
=3/8+1/8cos4x-1/2cos2x
对上式求不定积分,得
3x/8+1/32sin4x-1/4sin2x+C
即3x/8+1/32sin4x-1/4sin2x+C求导后得sin^4x
-1/4cos4x
-1/5cos5x