Question

Which of the following is the derivative of the function f(x) = x² - 1/x?

(a) 2x - 1/x²
(b) 2x + 1/x²
(c) x² - 1/x²
(d) x² + 1/x²

Answer 1

The derivative of the function f(x) = x² - 1/x is found by applying the power rule to each term, resulting in 2x + 1/x².

Step-by-step explanation:

The question is asking for the derivative of the function f(x) = x² - ⅛/x. The derivative of the function f(x) = x² - 1/x is found by applying the power rule to each term, resulting in 2x + 1/x². To find this derivative, we apply the power rule to both terms separately.

For the first term, x², the power rule tells us to multiply the exponent by the coefficient and reduce the exponent by one, resulting in 2x. For the second term, -⅛/x which is -x-1, applying the power rule involves multiplying the exponent by the coefficient and decreasing the exponent by one, which gives us +1/x². Hence, altogether, the derivative of the function f(x) is 2x + 1/x².