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nth derivative of y = sin2x cos3x is

nth derivative of y = sin2x cos3x is Correct Answer 1⁄8 cos⁡(x + nπ⁄2) –1⁄16 5n cos⁡(x + nπ⁄2) – 1⁄16 3n cos⁡(3x + nπ⁄2)

y = sin2x cos2x cos(x) y = 1⁄4 sin22x cos2x cos(x) y = 1⁄8 (2sin22x) cos(x) y = 1⁄8 (1 – cos4x) cos(x) y = 1⁄8 (1 – cos4x) cos(x) y = 1⁄8 cos(x) – 1⁄8 cos4x cos(x) y = 1⁄8 cos(x) – 1⁄16 (cos5x + cos(3x)) Now, nth derivative is yn = 1⁄8 cos⁡(x + nπ⁄2) – 1⁄16 5n cos⁡(x + nπ⁄2) – 1⁄16 3n cos⁡(3x + nπ⁄2).

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