What is the derivative of f(x) = x^3 - 4x^2 + 6x?
Correct Answer: 3x^2 - 8x + 6
- Step 1: Identify the function you want to differentiate. In this case, it is f(x) = x^3 - 4x^2 + 6x.
- Step 2: Recall the power rule for differentiation. The power rule states that if you have x^n, the derivative is n*x^(n-1).
- Step 3: Apply the power rule to each term in the function f(x).
- Step 4: Differentiate the first term, x^3. Using the power rule, the derivative is 3*x^(3-1) = 3x^2.
- Step 5: Differentiate the second term, -4x^2. Using the power rule, the derivative is -4*2*x^(2-1) = -8x.
- Step 6: Differentiate the third term, 6x. The derivative of x is 1, so the derivative is 6*1 = 6.
- Step 7: Combine all the derivatives from the previous steps. You get f'(x) = 3x^2 - 8x + 6.
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