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Differentiation Formulas Quiz

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Questions and Answers

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)?

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)?

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)?

∫ e^(2x) dx = (1/2)e^(2x) + C Signup and view all the answers

What is the integration formula for the function g(x) = √(2x + 1)?

∫ √(2x + 1) dx = (1/4)(2x + 1)^(3/2) + C Signup and view all the answers

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 Signup and view all the answers

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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Description

Test your knowledge of differentiation by finding the differentiation formulas for specific functions such as polynomial, square root, and exponential functions.