y=sin^4(3x)cos^3(4x)的导数怎么求?过程请详细点.

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y=sin^4(3x)cos^3(4x)的导数怎么求?过程请详细点.
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y=sin^4(3x)cos^3(4x)的导数怎么求?过程请详细点.
y=sin^4(3x)cos^3(4x)的导数怎么求?过程请详细点.

y=sin^4(3x)cos^3(4x)的导数怎么求?过程请详细点.
y'=cos^3(4x)[sin^4(3x)]'+sin^4(3x)[cos^3(4x)]'
=cos^3(4x)[4*3sin³(3x)cos(3x)]+sin^4(3x)[-3*4cos²(4x)sin(4x)]
=12sin³(3x)cos(3x)cos^3(4x)-12sin^4(3x)sin(4x)cos²(4x)
=12sin³(3x)cos²(4x)[cos(3x)cos(4x)-sin(3x)sin(4x)]
=12sin³(3x)cos²(4x)cos(7x) (应用三角函数的和差化积公式)

y'=[sin^4(3x)]'cos^3(4x)+sin^4(3x)[cos^3(4x)]'
=4sin^3(3x)*(sin3x)'*cos^3(4x)+sin^4(3x)*3cos^2(4x)*(cos4x)'
=4sin^3(3x)*cos(3x)*(3x)'*cos^3(4x)+sin^4(3x)*3cos^2(4x)*[-(sin4x)](4x)'
=12sin^3(3x)cos(3x)*cos^3(4x)-12sin^4(3x)*cos^2(4x)*(sin4x)

使用软件计算得：
4*(3*cos(3*x))*sin(3*x)^3*cos(4*x)^3+sin(3*x)^4*(3*(-4*sin(4*x))*cos(4*x)^2)

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