Final answer:
The derivative of the function f(x) = 2x² + 1/x is f'(x) = 4x - 1/x², found by applying the power rule and the derivative of an inverse function.
Step-by-step explanation:
The student asked to find the derivative of the function f(x) = 2x² + 1/x. To find this, we will apply the power rule and the derivative of the inverse function.
The power rule states that the derivative of x to the power of n is n times x to the power of (n-1). The derivative of 1/x, which is x to the power of -1, is -1 times x to the power of -2, or -1/x².
Therefore, the derivative f'(x) is:
- 4x for the 2x² term,
- -1/x² for the 1/x term.
Adding these together, we find the derivative f'(x) = 4x - 1/x².