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Question
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
x4 (5 sin x – 3 cos x)
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Solution
∵ (uv)' = u'v + uv'
∴ `d/dx[x^4(5 sinx - 3cosx)] = (d/dx x^4)(5sinx - 3cosx) + x^4 d/dx(5 sinx - 3 cosx)`
= 4x3 (5 sin x − 3 cos x) + x4 [5 cos x + 3 sin x]
= 20 x3 sin x - 12x3 cos x + 5x4 cos x + 3x4 sin x
= x3 sin x (20 + 3x) + x3 cos x (5x - 12)
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