Answer
$$ \frac{dy}{dx}=\frac{3}{\big(x^2+1\big)^{3/2}}$$
Work Step by Step
Step-1: Differentiate the following equation with respect to $x$,
$$y = \frac{3x}{\sqrt{x^2+1}}$$
,we get,
$$\frac{dy}{dx} = \frac{\big(\sqrt{x^2+1}\big)\frac{d}{dx}(3x)-(3x)\frac{d}{dx}\big(\sqrt{x^2+1}\big)}{\big(\sqrt{x^2+1}\big)^2}$$
$$\implies \frac{dy}{dx}=\frac{3\big(\sqrt{x^2+1}\big)-(3x)\frac{x}{\sqrt{x^2+1}}}{x^2+1}$$
Step-2: Simplify the above the equation,
$$\frac{dy}{dx}=\frac{\frac{3x^2+3-3x^2}{\sqrt{x^2+1}}}{x^2+1}$$
$$\implies \frac{dy}{dx}=\frac{3}{\big(x^2+1\big)^{3/2}}$$
