differentiate (x^2+1)^3 — step-by-step solution

Let's differentiate:

{({(x^{2} + 1)}^{3})}^{'}

Apply the differentiation rule:

{(f^{n})}^{'} = n \cdot {(f)}^{'} \cdot f^{(n - 1)}

with f =

x^{2} + 1

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

ℹ

(x^2+1)'

(x^2)' + 0

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

ℹ

(x^2)' + 0

(x^2)'

‖

(x^2)'

2 x

3 \cdot 2 x \cdot {(x^{2} + 1)}^{2}

▷Answer: $6 x \cdot {(x^{2} + 1)}^{2}$