Question

Let f(x) = x² - 2x. (a) Find the derivative f ' of f.

Answer 1

The derivative of the function f(x) = x² - 2x is found using the power rule of differentiation and is 2x - 2.

Step-by-step explanation:

To find the derivative of the function f(x) = x² - 2x, we can use the power rule for differentiation. The power rule states that when you have a function of the form g(x) = x^n, the derivative g'(x) = nx^(n-1). Applying this to each term of the function separately:

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• The derivative of x² is 2x.
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• The derivative of -2x is -2.

Therefore, the derivative of f(x) or f '(x) is 2x - 2.