(√x_2x²)'

To solve (√x_2x²)', we can use the chain rule.

Let's break down the given expression step by step.

Let f(x) = √(x^2), and g(x) = x².

First, let's find the derivative of f(x) using the chain rule: f'(x) = (1/2) * (x^2)^(-1/2) * (2x) = x / √(x^2) = x / |x|.

Now, let's find the derivative of g(x): g'(x) = 2x.

Using the chain rule, the derivative of (√x_2x²)' is: (√x_2x²)' = f'(g(x)) * g'(x) = (x / |x|) * (2x).

Simplifying the expression, we get: (√x_2x²)' = 2x^2 / |x|.

Therefore, the derivative of (√x_2x²) is 2x^2 / |x|.