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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Differentiation

JEE Main · Mathematics · Differentiation

(d)/(d x) ^ -1 (3 x-4 x^3) is equal to

ddxsin⁡−1(3x−4x3)isequalto\frac{d}{d x} \sin ^{-1} \left(3 x-4 x^3\right) is equal to

Options

  1. A34−x2\frac{3}{\sqrt{4-x^2}}
  2. B31−x2\frac{3}{\sqrt{1-x^2}}
  3. C14−x2\frac{1}{\sqrt{4-x^2}}
  4. D−14−x2-\frac{1}{\sqrt{4-x^2}}

Correct answer

B. 31−x2\frac{3}{\sqrt{1-x^2}}

Step-by-step solution

ddx{sin⁡−1(3x−4x3)} Put x=sin⁡θ⇒θ=sin⁡−1x=ddx{sin⁡−1(3sin⁡θ−4sin⁡3θ)}=ddx{sin⁡−1sin⁡3θ}=ddx{3θ}=3ddxsin⁡−1x=31−x2\begin{aligned} & \frac{d}{d x}\left\{\sin ^{-1}\left(3 x-4 x^3\right)\right\} \\ & \text { Put } x=\sin \theta \\ & \Rightarrow \quad \theta=\sin ^{-1} x \\ & =\frac{d}{d x}\left\{\sin ^{-1}\left(3 \sin \theta-4 \sin ^3 \theta\right)\right\} \\ & =\frac{d}{d x}\left\{\sin ^{-1} \sin 3 \theta\right\} \\ & =\frac{d}{d x}\{3 \theta\}=3 \frac{d}{d x} \sin ^{-1} x=\frac{3}{\sqrt{1-x^2}} \\ & \end{aligned}
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