Differentiate f(x) = 3x^3 - 5x^2 + 2; what is f'(x)?

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Multiple Choice

Differentiate f(x) = 3x^3 - 5x^2 + 2; what is f'(x)?

Explanation:
The derivative uses the power rule term-by-term: multiply the coefficient by the current exponent and lower the exponent by one, and the derivative of a constant is zero. For f(x) = 3x^3 - 5x^2 + 2: - d/dx of 3x^3 is 3 × 3 x^2 = 9x^2 - d/dx of -5x^2 is -5 × 2 x = -10x - d/dx of 2 is 0 Add them up: 9x^2 - 10x. The derivative is 9x^2 - 10x.

The derivative uses the power rule term-by-term: multiply the coefficient by the current exponent and lower the exponent by one, and the derivative of a constant is zero. For f(x) = 3x^3 - 5x^2 + 2:

  • d/dx of 3x^3 is 3 × 3 x^2 = 9x^2

  • d/dx of -5x^2 is -5 × 2 x = -10x

  • d/dx of 2 is 0

Add them up: 9x^2 - 10x. The derivative is 9x^2 - 10x.

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