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Best Answer

Trigonometric derivatives cycle, as shown.
y'=-2sin (2x)
y''=-4cos (2x)
y'''=8sin (2x)
y''''=16cos (2x)
So, for the 50th derivative, the co-efficient will be 2^(50).
The remainder of 50 divided by 4 is 2, so we know it corresponds with y''.
50th derivative of y=-2^(50)cos(2x)
Quadratic Formula.
r=(--4pm sqrt((-4)^(2)-4*1*1))/(2*1)
r=(4pm sqrt(16-4))/(2)
r=2pm sqrt(12)
r=2pm 2sqrt(3)
Result:
50th derivative of y=-2^(50)cos (2x)