Certainly! Let's break down the first step of finding the derivative of the function \( y = 10x^2 \):

1. **Identify the function**: The given function is \( y = 10x^2 \).

2. **Apply the power rule of differentiation**: The power rule states that if you have a function of the form \( f(x) = ax^n \), its derivative is \( f'(x) = anx^{n-1} \). 

    - Here, \( a = 10 \) and \( n = 2 \).

3. **Differentiate each term**: 

   \[
   \frac{d}{dx}(10x^2)
   \]

    - The coefficient \( 10 \) remains as it is.
    - Apply the power rule to \( x^2 \):

      \[
      \frac{d}{dx}(x^2) = 2x^{2-1} = 2x
      \]

    - Multiply the result by the coefficient \( 10 \):

      \[
      10 \cdot 2x = 20x
      \]

4. **Combine the results**: The derivative of the function \( y = 10x^2 \) is:

   \[
   \frac{dy}{dx} = 20x
   \]

So, the derivative of \( 10x^2 \) with respect to \( x \) is \( 20x \). This derivative represents the rate of change of \( y \) with respect to \( x \), indicating how sensitive \( y \) is to changes in \( x \).

Would you like more details or have any questions?

Here are some more questions you might want to explore:
1. How do you find the derivative of a sum of functions?
2. What is the product rule in differentiation?
3. How does the chain rule work in differentiation?
4. Can you explain the quotient rule in differentiation?
5. How do you interpret higher-order derivatives?

**Tip:** Always remember the basic differentiation rules (power, product, quotient, and chain rules) as they form the foundation for more complex calculus problems.

Learn how to find the derivative of the function y = 10x^2 using the power rule of differentiation. This problem covers differentiation techniques, specifically applying the power rule to derive the function's derivative with detailed steps provided.

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