Question

Differentiate

$(x+1)\sqrt{x^2+1}$

Answer 1

$\begin{array}{c}\frac{d}{dx}\left(\left(x+1\right)\sqrt{x^2+1}\right)=\left(x+1\right)\frac{d}{dx}\sqrt{x^2+1}+\sqrt{x^2+1}\frac{d}{dx}\left(x+1\right)\\ =\left(x+1\right)\cdot \frac{2x}{2\sqrt{x^2+1}}+\sqrt{x^2+1}\cdot 1\\ =\frac{x^2+x}{\sqrt{x^2+1}}+\sqrt{x^2+1}\end{array}$