y=sin^4x/4+cos^4x/4 求导
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y=sin^4x/4+cos^4x/4 求导
y=sin^4x/4+cos^4x/4 求导
y=sin^4x/4+cos^4x/4 求导
y=sin⁴x /4+cos⁴x /4
=(1/4)(sin⁴x+cos⁴x)
=(1/4)(sin⁴x+2sin²xcos²x+cos⁴x)-sin²xcos²x/2
=(1/4)(sin²x+cos²x)²-(2sinxcosx)²/8
=1/4-sin²(2x)/8
=(-1/16)[2sin²(2x)+1]+5/16
=(-1/16)cos(2x)+5/16
y'=(1/16)sin(2x)(2x)'=sin(2x)/8
提示:本题先用三角函数知识进行化简,然后再求导,比较简便.
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