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Question
Differentiate the following w.r.t. x :
cos3[cos–1(x3)]
Solution
Let y = cos3[cos–1(x3)]
Differentiating w.r.t. x, we get
`"dy"/"dx" = 3 cos^2 [cos^-1 (x^3)] . "d"/"dx"[cos(cos^-1 (x^3))]`
= `3 (x^3)^2 . "d"/"dx" [x^3]`
`"dy"/"dx" = 3(x^6) . 3(x^2)`
`"dy"/"dx" = 9x^8`
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