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In each of the following, differentiate the function and simplify your answer into the specified form.

(a) g(x)=x(4sin3x+6cos3x).

Answer: g'(x)=(Cx+D)sin3x+(Ex+F)cos3x with constants

C=_______,D=_______,E=_______, and F=______

(b) f(x)=x^(7) (7x-4)^5

f ' (x)=_________, which can be simplified to f ' (x)= x^(6) (7x-4)^(4) (Ax+B) with constants

A=_______ and B=_______

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It includes detailed steps of finding the derivatives of the functions.

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