已知Y=sin^43xcos^3 4x求Y的导数

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已知Y=sin^4*3xcos^3*4x求Y的导数已知Y=sin^4*3xcos^3*4x求Y的导数已知Y=sin^4*3xcos^3*4x求Y的导数y=sin⁴3xcos³4x

已知Y=sin^4*3xcos^3* 4x求Y的导数
已知Y=sin^4*3xcos^3* 4x求Y的导数

已知Y=sin^4*3xcos^3* 4x求Y的导数
y=sin⁴3xcos³4x
dy/dx=cos³4x*d(sin⁴3x)/dx + sin⁴3x*d(cos³4x)/dx
=cos³4x*d(sin⁴3x)/d(sin3x)*d(sin3x)/d(3x)*d(3x)/dx + sin⁴3x*d(cos³4x)/d(cos4x)*d(cos4x)/d(4x)*d(4x)/dx
=cos³4x*4sin³3x*cos3x*3 + sin⁴3x*3cos²4x*(-sin4x)*4
=12sin³3xcos3xcos²4x - 12sin⁴3xsin4xcos²4x
=12sin³3xcos²4xcos7x

y'=4sin^3(3x)cos(3x)3*cos^3(4x)+sin^4(3x)4[-sin^3(4x)]4

Y=sin^4*3xcos^3* 4x
y'=[(sin3x)^4]'*[(cos4x)^3]+[(sin3x)^4]*[(cos4x)^3]'
=4(sin3x)^3*(cos3x)*3*[(cos4x)^3]+[(sin3x)^4]*3*(cos4x)^2*(-sin4x)*4
=12(sin3xcos3xcos4x)^3-12(sin3x)^4(cos4x)^2sin4x

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