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

Let's perform the differentiation:

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

We differentiate using:

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

(where f =

x^{2} + 1

)

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

ℹ

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

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

‖

(x^2+1)'

(x^2)' + 0

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

▷Answer: $\frac{2 x}{x^{2} + 1}$