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We are tasked with finding the derivative of the function \( f(x) = (10\sqrt{x} + 3x)(4x^3 - 2x^2) \) using the product rule.

The product rule states that for two functions \( u(x) \) and \( v(x) \), the derivative of their product is:

\[
\frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)
\]

### Step 1: Define the two functions
We can define:
- \( u(x) = 10\sqrt{x} + 3x \)
- \( v(x) = 4x^3 - 2x^2 \)

###

Find the derivative of f(x) = (10√x + 3x)(4x^3 - 2x^2) using the product rule.

Learn how to find the derivative of f(x) = (10√x + 3x)(4x^3 - 2x^2) step by step using the product rule. This problem covers key differentiation concepts, including the product rule and power rule, suitable for Grades 11-12.

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