What is the derivative of f(x)= x^(3)*sin^(3)(3x)
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What is the derivative of f(x)= x^(3)*sin^(3)(3x)

[From: ] [author: ] [Date: 11-10-06] [Hit: ]
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f(x)= x^(3)*sin^(3)(3x)

=> f'(x)= 3*x^(2)*sin^(3)(3x) + x^3 * 3 * sin^2(3x) * cos(3x) * 3

=> f'(x)= 3*x^(2)*sin^(3)(3x) + 9 * x^3 * sin^2(3x) * cos(3x)

then if needed,

=> f'(x)= 3 * x^(2) * sin^2(3x) [sin(3x) + 3 * x * cos(3x)]

=> f'(x)= 3 * x^(2) * sin^2(3x) [sin(3x) + 3xcos(3x)]
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