对函数y=sin²x求导
y=sin²x\u6c42\u5bfc\u5148\u5bf9\uff08sin x\uff09² \u6574\u4f53\u6c42\u5bfc\uff0c\u4e3a2sin x\uff0c\u518d\u5bf9\u62ec\u53f7\u4e2d\u7684sin x\u6c42\u5bfc\uff0c\u4e3acos x\uff0c\u4e8c\u8005\u76f8\u4e58\uff0c\u5f97\u5230y = sin 2x\u7684\u5bfc\u6570\u4e3a 2sin x \u00b7 cos x = sin 2x
\u5f532kPi<=x<=2kPi+Pi\u65f6\uff0c\u5bfc\u6570\u4e3ay=3\uff08sinx\uff09\u7684\u5e73\u65b9\u4e58cosx\uff0c\u5f532kPi-Pi<=x<=2kPi\u65f6\uff0c\u5bfc\u6570\u4e3ay=-3\uff08sinx\uff09\u7684\u5e73\u65b9\u4e58cosx\u3002
令sinx=u则y=u²
y′=2uu′=2sinxcosx=sin2x
y'=cosxsinx+sinxcosx=2sinxcosx=sin2x
是y'=2cosx
y'=2sinxcosx=sin2x
一扩郐太太太太太太太太太太太
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