Step 1: Identify the function you want to differentiate, which is f(x) = 4x^5 - 2x^3 + x.
Step 2: Recall the power rule for differentiation. The power rule states that if you have a term in the form of ax^n, the derivative is a * n * x^(n-1).
Step 3: Differentiate the first term, 4x^5. Using the power rule, the derivative is 4 * 5 * x^(5-1) = 20x^4.
Step 4: Differentiate the second term, -2x^3. Using the power rule, the derivative is -2 * 3 * x^(3-1) = -6x^2.
Step 5: Differentiate the third term, x. This can be written as 1x^1. Using the power rule, the derivative is 1 * 1 * x^(1-1) = 1.
Step 6: Combine all the derivatives from Steps 3, 4, and 5. So, f'(x) = 20x^4 - 6x^2 + 1.
Power Rule – The power rule states that the derivative of x^n is n*x^(n-1).
Polynomial Differentiation – Differentiating polynomial functions involves applying the power rule to each term.
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