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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
The derivative of $\tan ^{-1}\left(x^2\right)$ w.r.t. $x$ is :
  • A
    $\frac{x}{1+x^4}$
  • B
    $\frac{2 x}{1+x^4}$
  • C
    $-\frac{2 x}{1+x^4}$
  • D
    $\frac{1}{1+ x ^4}$
✓

Answer

Let $y=\tan ^{-1}\left(x^2\right)$
$\Rightarrow \frac{d y}{d x}=\frac{d}{d x}\left(\tan ^{-1}\left(x^2\right)\right)=\frac{1}{1+\left(x^2\right)^2} \times 2 x=\frac{2 x}{1+x^4}$

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