Differential equationsFind the 50th derivative of y=cos 2x.
8 months ago
Find the 50th derivative of y=cos 2x.
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Best Answer
carlosmenciaconcertverizoncenter Staff answered 8 months ago
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)
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