differentiate sqrt(x^2+1) — step-by-step solution

Let's perform the differentiation:

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

Apply the differentiation rule:

{(\sqrt{f})}^{'} = {(f)}^{'} \cdot \frac{1}{2 \sqrt{f}}

with f =

x^{2} + 1

{(x^{2} + 1)}^{'} \cdot \frac{1}{2 \cdot \sqrt{x^{2} + 1}}

ℹ

(x^2+1)' \cdot \frac{1}{2 \cdot \sqrt{x^{2} + 1}}

\frac{(x^2+1)'}{2 \cdot \sqrt{x^{2} + 1}}

‖

(x^2+1)'

(x^2)' + 0

\frac{{(x^{2})}^{'} + 0}{2 \cdot \sqrt{x^{2} + 1}}

ℹ

(x^2)' + 0

(x^2)'

‖

(x^2)'

2 x

\frac{2 x}{2 \cdot \sqrt{x^{2} + 1}}

▷Result: $\frac{x}{\sqrt{x^{2} + 1}}$