AP Calculus AB: Chapter 4 Practice Test
This set of flashcards covers the fundamental derivatives of simple functions including constants, polynomials, and root functions. It provides quick practice on applying basic differentiation rules such as the power rule and the derivative of constants and square roots.
What is the derivative of the function f (x) = 5?
0
Key Terms
What is the derivative of the function f (x) = 5?
0
What is the derivative of the function f (x) = 2x?
2
What is the derivative of the function f(x)=−1/4x^6?
3/2x^7
Calculate f′(x) if f(x)=2x^9+8x^3+5.
18x ^8 + 24x ^2
What is the derivative of the function f(x)=−6x^2−3x^2−6x?
−12x+6/x^3−6
What is the derivative of the function f(x)=√x?
1/2√x
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| Term | Definition |
|---|---|
What is the derivative of the function f (x) = 5? | 0 |
What is the derivative of the function f (x) = 2x? | 2 |
What is the derivative of the function f(x)=−1/4x^6? | 3/2x^7 |
Calculate f′(x) if f(x)=2x^9+8x^3+5. | 18x ^8 + 24x ^2 |
What is the derivative of the function f(x)=−6x^2−3x^2−6x? | −12x+6/x^3−6 |
What is the derivative of the function f(x)=√x? | 1/2√x |
Compute the derivative of the function f (x) = (2x ^2 + 3) (4x − 6). | 4x (4x − 6) + 4 (2x^ 2 + 3) |
Compute the derivative of the function. f(x)=(3x^2+1x)(2x^3−5x+7) | (6x−1/x^2)(2x^3−5x+7)+(3x^2+1x)(6x^2−5) |
Compute the derivative of the function f(x) = (−3x^4+5x^2−√x+3)(x^−2−6x) | (-12x^3+10x−1/2x^−1/2)(x^−2−6x) +(-3x^4+5x^2−√x+3)(-2x^−3−6) |
Compute the derivative of the function f(x)=√x(4−x^2). | 4−5x^2 / 2x^1/2 |
Compute the derivative of the function f(x)=x−1/x+1. | 2/(x+1)^2 |
Compute the derivative of the function f(x)=1/x^2−x+2. | −2x+1 / (x^2−x+2)^2 |
Compute the derivative of the function f(x)=√x−1/√x+1. | 1/√x(√x+1)^2 |
Compute the derivative of the function f(x)=(x^2+x−3)^4 | 4(x^2+x−3)^3(2x+1) |
Compute the derivative of the function f(x)=(5x^3−4x+1/x)^6 | 6(5x^3−4x+1/x)^5(15x^2−4−x^−2) |
Compute the derivative of the function f(x) = (x^2−3x+4 / 2x+3)10 | (10(x^2−3x+4/2x+3)^9) (2x^2+6x−17/(2x+3)^2) |
Compute the derivative of the function f(x)=(x^2−1)^4 / x^2+1. | 2x(x^2−1)^3(3x^2+5) / (x^2+1)^2 |
Compute the derivative of the function f(x)=1/√4x^2−5. | −4x / (4x^2−5)√4x^2−5 |
Compute the derivative of the function f(x)=(x+1/x)^3/5 | 3/5(x+x^−1)^−2/5(1−x^−2) |
Compute the derivative of the function f(x)=(x^2−x)^3(3x+1) / x^4+2x^2−1. | (x^4+2x^2−1)[3(x^2−x)^2(2x−1)(3x+1) + 3(x^2−x)^3] −(x^2−x)^3(3x+1)(4x^3+4x) / (x^4+2x^2−1)^2 |