Find the derivative of f(x) = x^3 - 4x^2 + 6x.
Correct Answer: f'(x) = 3x^2 - 8x + 6
- Step 1: Identify the function you want to differentiate, which 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: For the first term x^3, the derivative is 3*x^(3-1) = 3x^2.
- Step 5: For the second term -4x^2, the derivative is -4*2*x^(2-1) = -8x.
- Step 6: For the third term 6x, the derivative is 6*1*x^(1-1) = 6.
- Step 7: Combine all the derivatives from the previous steps to get the final derivative: f'(x) = 3x^2 - 8x + 6.
- Power Rule – The power rule states that the derivative of x^n is n*x^(n-1).
- Polynomial Derivatives – Finding the derivative of polynomial functions involves applying the power rule to each term.
