The process for solving the derivative of f(x) = 1/2x^2 + 3x^3 is to first use the power rule for both terms. This means multiplying the coefficient by the exponent, subtracting 1 from the exponent, and then bringing down the variable. The final result will be the derivative of the function.
To check if your answer for the derivative is correct, you can take the derivative again and see if it matches the original function. Another method is to plug in a few values for x and see if the derivative and the original function give the same value.
No, you cannot use the product rule to find the derivative of f(x) = 1/2x^2 + 3x^3. The product rule is used for functions that are multiplied together, while this function is a sum of terms.
Yes, there is a shortcut for finding the derivative of polynomial functions called the power rule. This rule states that the derivative of a term with a variable raised to a power is the coefficient multiplied by the exponent, with the exponent reduced by 1 and the variable brought down.
No, the constant term does not affect the derivative of a polynomial function. The power rule only applies to terms with a variable raised to a power, so the constant term can be disregarded when finding the derivative.