# How do you differentiate f(x)=x sec kx^2  using the chain rule?

$\frac{d}{\mathrm{dx}} x \sec k {x}^{2} = 2 {x}^{2} \sec k {x}^{2} \left(\tan k {x}^{2} + 1\right)$
Assuming $k \in \mathbb{R}$ and is independent of x, we may use the product rule to write
$\frac{d}{\mathrm{dx}} x \sec k {x}^{2} = x \cdot \sec k {x}^{2} \tan k {x}^{2} \cdot 2 x + \sec k {x}^{2}$