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Cos5x

复合函数求导规则 -5sin5x

链式法则:dy/dx = dy/du * du/dx y = sin5x 所以dy/dx = d(sin5x)/d(5x) * d(5x)/dx = cos5x * 5 = 5cos5x 这函数分为y = sinu和u = 5x两部分的 每个都求导然后相乘

积化和差:cosacosb=1/2*[cos(a+b)+cos(a-b)] cos5xcos7x=1/2*[cos(5+7)x+cos(5-7)x]=1/2*[cos12x+cos2x] ∴∫cos5xcos7xdx =1/2∫(cos12x+cos2x)dx =1/2∫cos12xdx+1/2∫cos2xdx =1/2*1/12*∫cos12xd(12x)+1/2*1/2*∫cos2xd(2x) =1/24*sin12x+1/4*sin2x+C

cos5x-cos3x =cos(4x+x)-cos(4x-x) =cos4xcosx-sin4xsinx-cos4xcosx-sin4xsinx =-2sin4xsinx 如果不懂,请追问,祝学习愉快!

见图

cos2xcos3x =cos3xcos2x =(1/2){cos(3x+2x)+cos(3x-2x)} =1/2(cos5x+cosx)

使用积化和差公式 sinAcosB=(1/2)*sin(A+B)+ (1/2)*sin(A-B) 所以得到 sin2xcos5x=(1/2)*sin(5x)- (1/2)*sin(3x) 那么积分就得到 ∫(1/2)*sin(5x)- (1/2)*sin(3x) dx =1/10 *∫sin(5x) d(5x) -1/6 *∫sin(3x) d(3x) = -1/10 *cos(5x) +1/6 *cos(3x)...

(cos5xcos3x)' =(-5sin5x)cos3x+(-3sin3x)cos5x =-5sin5xcos3x-3sin3xcos5x

cosx*cos2x*cos4x = 2 sinx*cosx*cos2x*cos4x / (2sinx) = sin2x * cos2x *cos4x /(2sinx) =......= sin8x / (8sinx) cos3x*cos5x =(1/2) ( cos8x +cos2x) 原式= (1/16) (1/sinx) [ sin8x cos8x + sin8xcos2x ] = (1/32) (1/sinx) [ sin16x + si...

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