Final answer:
To differentiate y = 3 In 2x + 6x², apply the power rule and the constant multiple rule. The derivative is y' = 3/x ln(2x) + 12x.
Step-by-step explanation:
To differentiate y = 3 In 2x + 6x², we need to apply the power rule and the constant multiple rule. The power rule states that when differentiating a function of the form f(x) = ax^n, the derivative is given by f'(x) = nax^(n-1). The constant multiple rule states that when differentiating a function of the form g(x) = cf(x), where c is a constant, the derivative is given by g'(x) = cf'(x).
Applying these rules to the given function:
- The derivative of 3 In 2x is 3 * ln(2x) * (1/(2x)) = 3/x ln(2x).
- The derivative of 6x² is 12x.
Therefore, the derivative of y = 3 In 2x + 6x² is y' = 3/x ln(2x) + 12x.