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Questions and Answers
What is the differentiation formula for the function f(x) = x^3 + 2x^2 - 5x + 3?
What is the differentiation formula for the function f(x) = x^3 + 2x^2 - 5x + 3?
- f'(x) = 3x^2 + 4x
- f'(x) = 3x^2 + 2x
- f'(x) = 3x^2 + 2x - 5
- f'(x) = 3x^2 + 4x - 5 (correct)
What is the differentiation formula for the function g(x) = √(2x + 1)?
What is the differentiation formula for the function g(x) = √(2x + 1)?
- g'(x) = 1/√(2x)
- g'(x) = √(2x + 1)
- g'(x) = 1/√(2x + 1) (correct)
- g'(x) = 1/2√(2x + 1)
What is the differentiation formula for the function h(x) = e^(2x)?
What is the differentiation formula for the function h(x) = e^(2x)?
- h'(x) = 2e^(2x) + C
- h'(x) = 2e^(2x) (correct)
- h'(x) = e^(2x) + C
- h'(x) = e^(2x)
What is the integration formula for the function h(x) = e^(2x)?
What is the integration formula for the function h(x) = e^(2x)?
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What is the integration formula for the function g(x) = √(2x + 1)?
What is the integration formula for the function g(x) = √(2x + 1)?
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What is the integration formula for the function f(x) = x^3 + 2x^2 - 5x + 3?
What is the integration formula for the function f(x) = x^3 + 2x^2 - 5x + 3?
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Study Notes
Differentiation Formulas
- For the function f(x) = x^3 + 2x^2 - 5x + 3, the differentiation formula is f'(x) = 3x^2 + 4x - 5.
- For the function g(x) = √(2x + 1), the differentiation formula is g'(x) = 1 / (√(2x + 1)) * 2/2.
- For the function h(x) = e^(2x), the differentiation formula is h'(x) = 2e^(2x).
Integration Formulas
- For the function h(x) = e^(2x), the integration formula is ∫h(x)dx = (1/2)e^(2x) + C.
- For the function g(x) = √(2x + 1), the integration formula is ∫g(x)dx = (2/3)(2x + 1)^(3/2) + C.
- For the function f(x) = x^3 + 2x^2 - 5x + 3, the integration formula is ∫f(x)dx = (1/4)x^4 + (2/3)x^3 - (5/2)x^2 + 3x + C.
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