Find the derivative of cos3x by the first principle .

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y=cos3xLet f(x)=cos3x.Then f(x+h)=cos3x+hddx(f(x))=limh0fx+h-fxh=limh0cos3x+h-cos3xh=limh0-2sin3x+3h+3x2sin3x+3h-3x2h=limh0-2sin6x+3h2sin3h2h=-2limh0sin6x+3h2×limh0 sin32hh=-2sin3x×32=-3sin3x
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