Question

Differentiate $y=\sqrt{1+x^2}$ w.r.t $x$

Answer 1

$y=\sqrt{1+x^2}$

$y^2=1+x^2$

$\Rightarrow 2y\frac{dy}{dx}=2x$

$\Rightarrow \frac{dy}{dx}=\frac{x}{y}$

$\therefore \frac{dy}{dx}=\frac{x}{\sqrt{1+x^2}}$