Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the derivative of √x.
f(x) = 5x³

Verified step by step guidance

1. Step 1: Identify the function for which you need to find the derivative. Here, the function is \( f(x) = 5x^3 \).
2. Step 2: Recall the power rule for differentiation, which states that if \( f(x) = ax^n \), then \( f'(x) = anx^{n-1} \).
3. Step 3: Apply the power rule to the function \( f(x) = 5x^3 \). Here, \( a = 5 \) and \( n = 3 \).
4. Step 4: Differentiate the function using the power rule: \( f'(x) = 5 \times 3x^{3-1} \).
5. Step 5: Simplify the expression obtained from differentiation: \( f'(x) = 15x^2 \).