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Question
Differentiate the following w.r.t. x : cos–1(3x – 4x3)
Solution
Let y = cos–1(3x – 4x3)
Put x = sinθ.
Then θ = sin–1x
∴ y = cos–1(3sinθ - 4sin3θ)
= cos–1(sin3θ)
= `cos^-1[cos(pi/2 - 3θ)]`
= `pi/(2) - 3θ`
= `pi/(2) - 3sin^-1x`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(pi/2 - 3sin^-1x)`
= `"dy"/"dx"(pi/2) - 3"d"/"dx"(sin^-1x)`
= `0 - 3 xx 1/sqrt(1 - x^2)`
= `(-3)/sqrt(1 - x^2)`.
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