Answer
$\frac{dy}{dx}=2x\sec^2(x^2)$
Work Step by Step
Considering $u=x^2$, the function can be written as $y=\tan (u)$.
We have $y=f(g(x))$ where $g(x)=x^2$ and $f(u)=\tan (u)$.
Then,
$\frac{dy}{dx}=\frac{dy}{du}\cdot \frac{du}{dx}$ (By the chain rule)
$=\frac{d}{du}(\tan (u))\cdot \frac{d}{dx}(x^2)$ (Use the derivative for trigonometric function)
$=\sec^2(u)\cdot 2x$
$=\sec^2(x^2)\cdot 2x$
$=2x\sec^2(x^2)$
Thus,
$\frac{dy}{dx}=2x\sec^2(x^2)$
