Answer:
[tex]\frac{dy}{dx}=\frac{x}{\sqrt {x^2+1}}[/tex]
Step-by-step explanation:
We want to find:
[tex]\frac{dy}{dx} \\y=\sqrt u\\\frac{d}{dx}(\sqrt{u})[/tex]
Given that:
[tex]u=x^2+1[/tex]
Applying the chain rule:
[tex]\frac{dy}{dx}=\frac{dy}{du}*\frac{du}{dx}[/tex]
Solving dy/du:
[tex]\frac{dy}{du}=\frac{d}{du}(\sqrt u)\\\frac{dy}{du}=\frac{1}{2\sqrt u}[/tex]
Solving du/dx:
[tex]\frac{d}{dx}(x^2+1) = 2x[/tex]
Therefore, dy/dx is determined by:
[tex]\frac{dy}{dx}=\frac{1}{2\sqrt u}*2x \\\frac{dy}{dx}=\frac{x}{\sqrt u}\\\frac{dy}{dx}=\frac{x}{\sqrt {x^2+1}}[/tex]
