Answer
\[ \frac{dy}{dx}=\frac{2x}{1+x^4}\]
Work Step by Step
\[y=\tan ^{-1} (x^2)\]
\[\Rightarrow \tan y=x^2\;\;\;...(1)\]
Differentiate (1) implicitly with respect to $x$
\[\sec ^2 y\frac{dy}{dx}=2x\]
\[\frac{dy}{dx}=\frac{2x}{\sec^2 y}\]
\[\Rightarrow \frac{dy}{dx}=\frac{2x}{1+\tan ^2 y}\]
Using (1)
\[\Rightarrow \frac{dy}{dx}=\frac{2x}{1+x^4}\]
Hence \[ \frac{dy}{dx}=\frac{2x}{1+x^4}\]
