AP Calculus AB: Chapter 4 Test
This set of flashcards focuses on finding derivatives of polynomial functions, demonstrating the use of the power rule for different powers of π₯ x. It includes basic examples ranging from linear functions to higher-degree polynomials.
What is the derivative of the function fβ(x) = xβ?
1
Key Terms
What is the derivative of the function fβ(x) = xβ?
1
What is the derivative of the function
fβ(x) = 3xβ^9?
27x^8
What is the derivative of the function f(x)=β2/3 *x^3?
β2xβ^2
Calculate fβ²(x) if f(x)=x^4+2x.
4x^3+2
What is the derivative of the function
f(x)=10/x^2+3/x^4β60x?
-20/x^3β12/x^5β60
What is the derivative of the function f(x)=βx+ ^3βx?
1/2x^β1/2+1/3x^β2/3
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| Term | Definition |
|---|---|
What is the derivative of the function fβ(x) = xβ? | 1 |
What is the derivative of the function fβ(x) = 3xβ^9? | 27x^8 |
What is the derivative of the function f(x)=β2/3 *x^3? | β2xβ^2 |
Calculate fβ²(x) if f(x)=x^4+2x. | 4x^3+2 |
What is the derivative of the function f(x)=10/x^2+3/x^4β60x? | -20/x^3β12/x^5β60 |
What is the derivative of the function f(x)=βx+ ^3βx? | 1/2x^β1/2+1/3x^β2/3 |
Compute the derivative of the function fβ(x) = (5x^β4 β 2x^β2 + 7x + 4) (2xβ^2 β 5). | (20x^β3 β 4x + 7) (2xβ^2 β 5) + 4x (5x^β4 β 2x^β2 + 7x + 4) |
Compute the derivative of the function fβ(x) = (2xβ^2 + 3)^2. | 8x (2xβ^2 + 3) |
Compute the derivative of the function f β(x) = (βx + 3xβ^2 β xβ^β2β)(3x β x^ββ1β). | (β1 + 6x + 2xβ^β3β) (3x β x^ββ1β) + (βx + 3xβ^2 β x^ββ2β) (3 + xβ^β2β) |
Compute the derivative of the function f(x)=xβx^2 / 3x+5. | (1β2x)(3x+5)β3(xβx^2) / (3x+5)^2 |
Compute the derivative of the function f(x)=x^2+xβ3 / x^3+5. | (2x+1)(x^3+5)β(3x^2)(x^2+xβ3) / (x^3+5)^2 |
Compute the derivative of the function f(x)=1/(x^2β1)^2. | β4x/(x^2β1)^3 |
Compute the derivative of the function f(x)=x^3+3x^2β5 / βx+1. | (3x^2+6x)(βx+1)β(x^3+3x^2β5)1/2x^β1/2 / (βx+1)^2 |
Compute the derivative of the function f(x) = (x^4 - 2x^2 + 7x + 4)^3 | 3(x^4β2x^2+7x+4)^2(4x^3β4x+7)` |
Compute the derivative of the function f(x)=(x+1 / xβ1)^5 | β10(x+1)^4 / (xβ1)^6 |
Compute the derivative of the function f(x)=(3x^2βx+1 / x^2+1)^7. | 7(3x^2βx+1 / x^2+1)^6 (x^2+4xβ1 / (x^2+1)^2) |
Compute the derivative of the function f(x) = (4x^2-x+1)^7 (1+βx) | 7(4x^2-x+1)^6(8x-1)(1+βx) + (4x^2-x+1)^7(1/2x^-1/2) |
Compute the derivative of the function f(x)=2x / (3x^2+2)^3/2. | 2(3x^2+2)^3/2β18x^2(3x^2+2)^1/2 / (3x^2+2)^3 |
Compute the derivative of the function f(x)=βx^2+1/x^2β1 | -(x^2+1/x^2β1)^-1/2 * 2x(x^2β1)^2 |
Compute dy/dx for y=(3x^2βx)^2 / 3βx^2 | 2(3x^2βx)(6xβ1)(3βx^2)+2x(3x^2βx)^2(3βx^2)^2 |