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What is the derivative of f(x) = x^3 - 4x^2 + 6x?
What is the derivative of f(x) = x^3 - 4x^2 + 6x?
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Q1
What is the derivative of f(x) = x^3 - 4x^2 + 6x?
3x^2 - 8x + 6
3x^2 + 8x + 6
2x^2 - 4x + 6
3x^2 - 4x + 6
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The derivative f'(x) = d/dx(x^3 - 4x^2 + 6x) = 3x^2 - 8x + 6.
Questions & Step-by-step Solutions
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Q
Q: What is the derivative of f(x) = x^3 - 4x^2 + 6x?
Solution:
The derivative f'(x) = d/dx(x^3 - 4x^2 + 6x) = 3x^2 - 8x + 6.
Steps: 7
Show Steps
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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