Question

Find the derivative of √(3x^3 + 2x )

Answer 1

Rewrite as
\[\large (3x^3+2x)^{1/2}\]
and use chain rule.

Answer 2

\[1/2(3x^3+2x)^-1/2 (9x^2 + 2)\]

Answer 3

Exactly.
That can be rewritten as
\[\large \frac{9x^2+2}{2\sqrt{3x^3+2x}}\]