Dirty differentiation

Calculus Level 3

If the derivative d/dtd/dt of cos4(t)+cos(t)4cos^{4}(t) + cos(t)^{4} can be written as (asin(t))(cosb(t))(ct3)(sin(td)) (a sin (t))(cos^{b}(t))-(ct^{3})(sin(t^{d})). Find the value ofa+b+c+da+b+c+d

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