What this deck covers
This deck focuses on Applying The Power Rule, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus AB.
AP Calculus AB Flashcards: Applying The Power Rule
Study Applying The Power Rule in AP Calculus AB with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.
AP Calculus AB
Applying The Power Rule
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QUESTION
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Differentiate f(x)=x6−x2 using the Power Rule.
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ANSWER
f′(x)=6x5−2x. Differentiate each term: 6x5−2x.
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Flashcard 1: Differentiate f(x)=x6−x2 using the Power Rule.
Answer: f′(x)=6x5−2x. Differentiate each term: 6x5−2x.
Flashcard 2: Differentiate f(x)=2x5+3x3−x2 using the Power Rule.
Answer: f′(x)=10x4+9x2−2x. Differentiate each term using Power Rule.
Flashcard 3: What is the derivative of f(x)=−5x0.5?
Answer: f′(x)=−2.5x−0.5. Apply Power Rule: −5⋅0.5⋅x0.5−1=−2.5x−0.5.
Flashcard 4: Find the derivative of f(x)=x0.
Answer: f′(x)=0. x0=1, which is constant, so derivative is 0.
Flashcard 5: Differentiate f(x)=15x1/4 using the Power Rule.
Answer: f′(x)=415x−3/4. Apply Power Rule: 15⋅41⋅x41−1=415x−3/4.
Flashcard 6: What is the derivative of f(x)=8x−4?
Answer: f′(x)=−32x−5. Apply Power Rule: 8⋅(−4)⋅x−4−1=−32x−5.
Flashcard 7: What is the derivative of f(x)=x2/3?
Answer: f′(x)=32x−1/3. Apply Power Rule: 32⋅x32−1=32x−1/3.
Flashcard 8: State the Power Rule for differentiation.
Answer: dxd[xn]=nxn−1. Fundamental differentiation rule: bring down exponent, subtract 1 from power.
Flashcard 9: Differentiate f(x)=x1/2 using the Power Rule.
Answer: f′(x)=21x−1/2. Apply Power Rule: 21⋅x21−1=21x−1/2.
Flashcard 10: What is the derivative of f(x)=x8?
Answer: f′(x)=8x7. Apply Power Rule: 8⋅x8−1=8x7.
Flashcard 11: Differentiate f(x)=5x7/4 using the Power Rule.
Answer: f′(x)=435x3/4. Apply Power Rule: 5⋅47⋅x47−1=435x3/4.
Flashcard 12: Differentiate f(x)=6x3+7x using the Power Rule.
Answer: f′(x)=18x2+7. Differentiate each term: 6⋅3x2+7⋅1=18x2+7.
Flashcard 13: What is the derivative of f(x)=−2x3?
Answer: f′(x)=−6x2. Apply Power Rule: −2⋅3⋅x3−1=−6x2.
Flashcard 14: Differentiate f(x)=8x2/5 using the Power Rule.
Answer: f′(x)=516x−3/5. Apply Power Rule: 8⋅52⋅x52−1=516x−3/5.
Flashcard 15: Find the derivative of f(x)=7x3/7 using the Power Rule.
Answer: f′(x)=3x−4/7. Apply Power Rule: 7⋅73⋅x73−1=3x−4/7.
Flashcard 16: Differentiate f(x)=x6−x2 using the Power Rule.
Answer: f′(x)=6x5−2x. Differentiate each term: 6x5−2x.
Flashcard 17: Differentiate f(x)=11x−2/5 using the Power Rule.
Answer: f′(x)=−522x−7/5. Apply Power Rule: 11⋅(−52)⋅x−52−1=−522x−7/5.
Flashcard 18: Differentiate f(x)=x1/3 using the Power Rule.
Answer: f′(x)=31x−2/3. Apply Power Rule: 31⋅x31−1=31x−2/3.
Flashcard 19: What is the derivative of f(x)=x2/3?
Answer: f′(x)=32x−1/3. Apply Power Rule: 32⋅x32−1=32x−1/3.
Flashcard 20: Differentiate f(x)=6x3+7x using the Power Rule.
Answer: f′(x)=18x2+7. Differentiate each term: 6⋅3x2+7⋅1=18x2+7.
Flashcard 21: What is the derivative of f(x)=7x−3?
Answer: f′(x)=−21x−4. Apply Power Rule: 7⋅(−3)⋅x−3−1=−21x−4.
Flashcard 22: Differentiate f(x)=x5 using the Power Rule.
Answer: f′(x)=5x4. Apply Power Rule: 5⋅x5−1=5x4.
Flashcard 23: Differentiate f(x)=x−2/3 using the Power Rule.
Answer: f′(x)=−32x−5/3. Apply Power Rule: −32⋅x−32−1=−32x−5/3.
Flashcard 24: Differentiate f(x)=x5 using the Power Rule.
Answer: f′(x)=5x4. Apply Power Rule: 5⋅x5−1=5x4.
Flashcard 25: Differentiate f(x)=x1/3 using the Power Rule.
Answer: f′(x)=31x−2/3. Apply Power Rule: 31⋅x31−1=31x−2/3.
Flashcard 26: Find the derivative of f(x)=x3.5 using the Power Rule.
Answer: f′(x)=3.5x2.5. Apply Power Rule: 3.5⋅x3.5−1=3.5x2.5.
Flashcard 27: Derive f(x)=x−1 using the Power Rule.
Answer: f′(x)=−x−2. Apply Power Rule: −1⋅x−1−1=−x−2.
Flashcard 28: Find the derivative of f(x)=x0.
Answer: f′(x)=0. x0=1, which is constant, so derivative is 0.
Flashcard 29: Differentiate f(x)=3x5/2−4x3/2 using the Power Rule.
Answer: f′(x)=215x3/2−6x1/2. Differentiate each term using Power Rule.
Flashcard 30: Differentiate f(x)=15x1/4 using the Power Rule.
Answer: f′(x)=415x−3/4. Apply Power Rule: 15⋅41⋅x41−1=415x−3/4.
Flashcard 31: Differentiate f(x)=2x4+3x2 using the Power Rule.
Answer: f′(x)=8x3+6x. Differentiate each term: 2⋅4x3+3⋅2x=8x3+6x.
Flashcard 32: Differentiate f(x)=x10 using the Power Rule.
Answer: f′(x)=10x9. Apply Power Rule: 10⋅x10−1=10x9.
Flashcard 33: Find the derivative of f(x)=x−5 using the Power Rule.
Answer: f′(x)=−5x−6. Apply Power Rule: −5⋅x−5−1=−5x−6.
Flashcard 34: What is the derivative of f(x)=−5x0.5?
Answer: f′(x)=−2.5x−0.5. Apply Power Rule: −5⋅0.5⋅x0.5−1=−2.5x−0.5.
Flashcard 35: Differentiate f(x)=3x5/2−4x3/2 using the Power Rule.
Answer: f′(x)=215x3/2−6x1/2. Differentiate each term using Power Rule.
Flashcard 36: Find f′(x) for f(x)=10x−0.5. Use the Power Rule.
Answer: f′(x)=−5x−1.5. Apply Power Rule: 10⋅(−0.5)⋅x−0.5−1=−5x−1.5.
Flashcard 37: Differentiate f(x)=3x4.5 using the Power Rule.
Answer: f′(x)=13.5x3.5. Apply Power Rule: 3⋅4.5⋅x4.5−1=13.5x3.5.
Flashcard 38: What is the derivative of f(x)=7x−3?
Answer: f′(x)=−21x−4. Apply Power Rule: 7⋅(−3)⋅x−3−1=−21x−4.
Flashcard 39: Find f′(x) for f(x)=10x−0.5. Use the Power Rule.
Answer: f′(x)=−5x−1.5. Apply Power Rule: 10⋅(−0.5)⋅x−0.5−1=−5x−1.5.
Flashcard 40: Differentiate f(x)=3x4.5 using the Power Rule.
Answer: f′(x)=13.5x3.5. Apply Power Rule: 3⋅4.5⋅x4.5−1=13.5x3.5.
Flashcard 41: Differentiate f(x)=x1/2 using the Power Rule.
Answer: f′(x)=21x−1/2. Apply Power Rule: 21⋅x21−1=21x−1/2.
Flashcard 42: Find the derivative of f(x)=x3.5 using the Power Rule.
Answer: f′(x)=3.5x2.5. Apply Power Rule: 3.5⋅x3.5−1=3.5x2.5.
Flashcard 43: Differentiate f(x)=2x4+3x2 using the Power Rule.
Answer: f′(x)=8x3+6x. Differentiate each term: 2⋅4x3+3⋅2x=8x3+6x.
Flashcard 44: Differentiate f(x)=9x−1/2 using the Power Rule.
Answer: f′(x)=−4.5x−3/2. Apply Power Rule: 9⋅(−21)⋅x−21−1=−4.5x−3/2.
Flashcard 45: Differentiate f(x)=x−2/3 using the Power Rule.
Answer: f′(x)=−32x−5/3. Apply Power Rule: −32⋅x−32−1=−32x−5/3.
Flashcard 46: What is the derivative of f(x)=x9?
Answer: f′(x)=9x8. Apply Power Rule: 9⋅x9−1=9x8.
Flashcard 47: Differentiate f(x)=x−3 using the Power Rule.
Answer: f′(x)=−3x−4. Apply Power Rule: −3⋅x−3−1=−3x−4.
Flashcard 48: What is the derivative of f(x)=8x−4?
Answer: f′(x)=−32x−5. Apply Power Rule: 8⋅(−4)⋅x−4−1=−32x−5.
Flashcard 49: Derive f(x)=x−1 using the Power Rule.
Answer: f′(x)=−x−2. Apply Power Rule: −1⋅x−1−1=−x−2.
Flashcard 50: What is the derivative of f(x)=7x2?
Answer: f′(x)=14x. Apply Power Rule: 7⋅2⋅x2−1=14x.
Flashcard 51: Find the derivative of f(x)=x3.3 using the Power Rule.
Answer: f′(x)=3.3x2.3. Apply Power Rule: 3.3⋅x3.3−1=3.3x2.3.
Flashcard 52: What is the derivative of f(x)=4x0?
Answer: f′(x)=0. 4x0=4, which is constant, so derivative is 0.
Flashcard 53: Find the derivative of f(x)=4x−2−3x−4. Use Power Rule.
Answer: f′(x)=−8x−3+12x−5. Differentiate each term: 4(−2)x−3−3(−4)x−5.
Flashcard 54: Differentiate f(x)=x−3 using the Power Rule.
Answer: f′(x)=−3x−4. Apply Power Rule: −3⋅x−3−1=−3x−4.
Flashcard 55: Differentiate f(x)=5 using the Power Rule.
Answer: f′(x)=0. Constant functions have derivative 0.
Flashcard 56: Find the derivative of f(x)=x3.3 using the Power Rule.
Answer: f′(x)=3.3x2.3. Apply Power Rule: 3.3⋅x3.3−1=3.3x2.3.
Flashcard 57: What is the derivative of f(x)=7x2?
Answer: f′(x)=14x. Apply Power Rule: 7⋅2⋅x2−1=14x.
Flashcard 58: Differentiate f(x)=x0.1 using the Power Rule.
Answer: f′(x)=0.1x−0.9. Apply Power Rule: 0.1⋅x0.1−1=0.1x−0.9.
Flashcard 59: What is the derivative of f(x)=4x0?
Answer: f′(x)=0. 4x0=4, which is constant, so derivative is 0.
Flashcard 60: Find the derivative of f(x)=6x−3/2 using the Power Rule.
Answer: f′(x)=−9x−5/2. Apply Power Rule: 6⋅(−23)⋅x−23−1=−9x−5/2.
Flashcard 61: Differentiate f(x)=11x−2/5 using the Power Rule.
Answer: f′(x)=−522x−7/5. Apply Power Rule: 11⋅(−52)⋅x−52−1=−522x−7/5.
Flashcard 62: What is the derivative of f(x)=x8?
Answer: f′(x)=8x7. Apply Power Rule: 8⋅x8−1=8x7.
Flashcard 63: What is the derivative of f(x)=−2x3?
Answer: f′(x)=−6x2. Apply Power Rule: −2⋅3⋅x3−1=−6x2.
Flashcard 64: What is the derivative of f(x)=x9?
Answer: f′(x)=9x8. Apply Power Rule: 9⋅x9−1=9x8.
Flashcard 65: Differentiate f(x)=9x−1/2 using the Power Rule.
Answer: f′(x)=−4.5x−3/2. Apply Power Rule: 9⋅(−21)⋅x−21−1=−4.5x−3/2.
Flashcard 66: Find the derivative of f(x)=x−5 using the Power Rule.
Answer: f′(x)=−5x−6. Apply Power Rule: −5⋅x−5−1=−5x−6.
Flashcard 67: Differentiate f(x)=5 using the Power Rule.
Answer: f′(x)=0. Constant functions have derivative 0.
Flashcard 68: Differentiate f(x)=8x2/5 using the Power Rule.
Answer: f′(x)=516x−3/5. Apply Power Rule: 8⋅52⋅x52−1=516x−3/5.
Flashcard 69: Find the derivative of f(x)=4x−2−3x−4. Use Power Rule.
Answer: f′(x)=−8x−3+12x−5. Differentiate each term: 4(−2)x−3−3(−4)x−5.
Flashcard 70: Differentiate f(x)=5x7/4 using the Power Rule.
Answer: f′(x)=435x3/4. Apply Power Rule: 5⋅47⋅x47−1=435x3/4.
Flashcard 71: Differentiate f(x)=2x5+3x3−x2 using the Power Rule.
Answer: f′(x)=10x4+9x2−2x. Differentiate each term using Power Rule.
Flashcard 72: Differentiate f(x)=x10 using the Power Rule.
Answer: f′(x)=10x9. Apply Power Rule: 10⋅x10−1=10x9.
Flashcard 73: Differentiate f(x)=13x−0.3 using the Power Rule.
Answer: f′(x)=−3.9x−1.3. Apply Power Rule: 13⋅(−0.3)⋅x−0.3−1=−3.9x−1.3.
Flashcard 74: Differentiate f(x)=x0.1 using the Power Rule.
Answer: f′(x)=0.1x−0.9. Apply Power Rule: 0.1⋅x0.1−1=0.1x−0.9.
Flashcard 75: Differentiate f(x)=13x−0.3 using the Power Rule.
Answer: f′(x)=−3.9x−1.3. Apply Power Rule: 13⋅(−0.3)⋅x−0.3−1=−3.9x−1.3.
Flashcard 76: Find the derivative of f(x)=6x−3/2 using the Power Rule.
Answer: f′(x)=−9x−5/2. Apply Power Rule: 6⋅(−23)⋅x−23−1=−9x−5/2.
Flashcard 77: Find the derivative of f(x)=7x3/7 using the Power Rule.
Answer: f′(x)=3x−4/7. Apply Power Rule: 7⋅73⋅x73−1=3x−4/7.