Question

If $y=\tan \left[\text{log}\right(x^2\left)\right]$, then $\frac{dy}{dx}$ is -

• A. $2x{\sec }^2\left[\text{log}\right(x^2\left)\right]$
• B. $\frac{2{\sec }^2\left[\text{log}\right(x^2\left)\right]}{x}$
• C. $x{\sec }^2\left[\text{log}\right(x^2\left)\right]$
• D. $\frac{1}{x^2}{\sec }^2\left[\text{log}\right(x^2\left)\right]$

Answer 1

The correct option is B $\frac{2{\sec }^2\left[\text{log}\right(x^2\left)\right]}{x}$

$y=\tan \left[\text{log}\right(x^2\left)\right]$ differentiate w.r.t $x$
$\frac{dy}{dx}=\frac{d}{dx}\left[\tan \right\{\text{log}\left(x^2\right)\left\}\right]$
$\frac{dy}{dx}=se{c}^2\left(\text{log}{x}^2\right).\frac{d}{dx}\left[\text{log}\right(x^2\left)\right]$
$\frac{dy}{dx}=se{c}^2\left(\text{log}{x}^2\right).\frac{1}{x^2}.\frac{d}{dx}\left(x^2\right)$
$\frac{dy}{dx}={\sec }^2\left(\text{log}{x}^2\right).\frac{1}{x^2}.2x$
$\frac{dy}{dx}=\frac{2}{x}.se{c}^2\left(\text{log}{x}^2\right)$