6 Questions
What is the differentiation formula for the function f(x) = x^3 + 2x^2 - 5x + 3?
f'(x) = 3x^2 + 4x - 5
What is the differentiation formula for the function g(x) = √(2x + 1)?
g'(x) = 1/√(2x + 1)
What is the differentiation formula for the function h(x) = e^(2x)?
h'(x) = 2e^(2x)
What is the integration formula for the function h(x) = e^(2x)?
∫ e^(2x) dx = (1/2)e^(2x) + C
What is the integration formula for the function g(x) = √(2x + 1)?
∫ √(2x + 1) dx = (1/4)(2x + 1)^(3/2) + C
What is the integration formula for the function f(x) = x^3 + 2x^2 - 5x + 3?
∫ (x^3 + 2x^2 - 5x + 3) dx = (1/4)x^4 + (2/3)x^3 - (5/2)x^2 + 3x + C
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.
Test your knowledge of differentiation by finding the differentiation formulas for specific functions such as polynomial, square root, and exponential functions.
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