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Differentiate the following w.r.t.x: cot3[log(x3)]

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Question

Differentiate the following w.r.t.x: cot3[log(x3)]

Sum
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Solution

Let y = cot3[log(x3)]

Differentiating w.r.t. x,we get,

`"dy"/"dx" = "d"/"dx"[cot(logx^3)]^3`

∴ `"dy"/"dx" = 3[cot(logx^3)]^2*"d"/"dx"[cot(logx^3)]`

∴ `"dy"/"dx" = 3cot^2[log(x^3)]*[-"cosec"^2(logx^3)]*"d"/"dx"(logx^3)`

∴ `"dy"/"dx" = -3cot^2[log(x^3)]*"cosec"^2[log(x^3)]*3"d"/"dx"(logx)`

∴ `"dy"/"dx" = -3cot^2[log(x^3)]*"cosec"^2[log(x^3)] * 3 xx 1/x`

∴ `"dy"/"dx" = (-9" cosec"^2[log(x^3)]*cot^2[log(x^3)]]/x`

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Chapter 1: Differentiation - Exercise 1.1 [Page 12]

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