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Question
Differentiate the following w.r.t.x: log[cos(x3 – 5)]
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Solution
Let y = log[cos(x3 – 5)]
Differentiating w.r.t. x, we get,
`"dy"/"dx" = "d"/"dx"{log[cos(x^3 - 5)]}`
= `(1)/(cos(x^3 - 5))."d"/"dx"[cos(x^3 - 5)]`
= `(1)/(cos(x^3 - 5)).[-sin(x^3 - 5)]."d"/"dx"(x^3 - 5)`
= –tan(x3 – 5) x (3x2 – 0)
= –3x2tan(x3 – 5).
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