Final answer:
To find the first and second derivatives of y = x² ln(5x), apply the chain rule and product rule.
Step-by-step explanation:
To find y' and y'' for the given y = x² ln(5x), we need to apply the chain rule and product rule.
- Using the chain rule, differentiate x² ln(5x) with respect to x: y' = 2x ln(5x) + x²(1/x) = 2x ln(5x) + x
- Using the product rule, differentiate y' with respect to x: y'' = 2 ln(5x) + 2x(1/x) + 1 = 2 ln(5x) + 3