Question

Find the derivative of $\tan (2x+3)$

Answer 1

Let $y=\tan (2x+3)$
We need to find derivative of $y$ w.r.t. $x$
i.e., $\frac{dy}{dx}=\frac{d\left(\tan \right(2x+3\left)\right)}{dx}$
$\Rightarrow \frac{dy}{dx}={\sec }^2(2x+3)\times \frac{d(2x+3)}{dx}$
$\{\text{using chain rule}\frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}\}$
$\Rightarrow \frac{dy}{dx}={\sec }^2(2x+3)\times 2$
​​​​​​​$\Rightarrow \frac{dy}{dx}=2{\sec }^2(2x+3)$