Question

$\frac{d}{d x} (tan a x) =$

Answer: $a {sec}^{2} a x$

\begin{array}{rclc} \frac{d}{d x} (tan a x) & = & \frac{d (tan (a x))}{d (a x)} \times \frac{d (a x)}{d x} \\ = & {sec}^{2} (a x) \times \frac{d (a x)}{d x} & \begin{array}{l} (∵ derivative of tan x \\ is {sec}^{2} x) \end{array} \\ = & {sec}^{2} (a x) \times a \times \frac{d (x)}{d x} & (∵ ’a’ is constant) \\ = & {sec}^{2} (a x) \times a \times 1 \\ = & a {sec}^{2} (a x) \cdot \end{array}

So, correct answer is option-2, $\to a {sec}^{2} a x$