Answer :
Final answer:
The derivative of the function f(x) = 2x^4 - 6x^3 + 1 is f'(x) = 8x^3 - 18x^2, calculated by applying the power rule to each term.
Explanation:
To find the derivative of the function f(x) = 2x^4 - 6x^3 + 1, we apply the power rule to each term. The power rule states that for a function of the form f(x) = axn, the derivative f'(x) is naxn-1. Therefore:
- The derivative of 2x^4 is 8x^3 (using the power rule: 4*2x^3).
- The derivative of -6x^3 is -18x^2 (using the power rule: 3*(-6)x^2).
- The derivative of the constant term 1 is 0, because the derivative of any constant is zero.
Adding these up, the derivative of the function, f'(x), is 8x^3 - 18x^2.
