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Question
Differentiate the following w.r.t.x: cos2[log(x2 + 7)]
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Solution
Let y = cos2[log(x2 + 7)]
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"{cos[log(x^2 + 7)]}^2`
= `2cos[log(x^2 + 7)]."d"/"dx"{cos[log(x^2 + 7)]}`
= `2cos[log(x^2 + 7)].{-sin[log(x^2 + 7)]}."d"/"dx"[log(x^2 + 7)]`
= `-2sin[log(x^2 + 7)].cos[log(x^2 + 7)] xx (1)/(x^2 + 7)."d"/"dx"(x^2 + 7)`
= `-sin[2log(x^2 + 7)] xx (1)/(x^2 + 7).(2x + 0)` ...[∵ 2sinx · cosx = sin2x]
= `(-2x.sin[2log(x^2 + 7)])/(x^2 + 7)`.
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