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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):
(ax2 + sin x) (p + q cos x)
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Solution
(uv)' = u'v + uv'
∴ `d/dx[(ax^2 + sin x)(p + q cos x)]`
= `[d/dx (ax^2 + sin x)](p + q cos x) + (ax^2 + sin x) d/dx (p + q cos x)`
= (2ax + cos x)(p + q cos x) + (ax2 + sin x)(−q sin x)
= (−q sin x) (ax2 + sin x) + (p + q cos x) (2ax + cos x)
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