Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55

CAL2.141 Term by Term Differentiation Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.141 Term by Term Differentiation. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.141 Term-by-Term Differentiation - Select the derivative power series and its interval implications. Standards: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Calculus II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related CAL2.141 Term by Term Differentiation skill assessments:

Problem 1Difficulty: Mastery

Let f(x)=∑_{n=1}^∞ (−1)ⁿ⁺¹(x−2)ⁿ/(n² 3ⁿ). Which f'(x) and interval of convergence are correct?

Af'(x)=∑_{n=1}^∞ (−1)ⁿ⁺¹(x−2)ⁿ/(n3ⁿ), interval [−1,5]

Bf'(x)=∑_{n=1}^∞ (−1)ⁿ(x−2)ⁿ⁻¹/(n3ⁿ), interval [−1,5)

Cf'(x)=∑_{n=1}^∞ (−1)ⁿ⁺¹(x−2)ⁿ⁻¹/3ⁿ, interval (−1,5)

Df'(x)=∑_{n=1}^∞ (−1)ⁿ⁺¹(x−2)ⁿ⁻¹/(n3ⁿ), interval (−1,5]

Solution & Explanation:Differentiating changes 1/n² to 1/n and lowers the exponent. At x=5 the derivative endpoint is alternating harmonic; at x=−1 it is harmonic, so the interval is (−1,5].

Problem 2Difficulty: Mastery

Let f(x)=∑_{n=0}^∞ (x−1)ⁿ/(n+1)!. What is f'(1) by term-by-term differentiation?

C1/2

Solution & Explanation:The derivative is ∑_{n=1}^∞ n(x−1)ⁿ⁻¹/(n+1)!. At x=1, only n=1 remains, giving 1/2! = 1/2.

Problem 3Difficulty: Mastery

A student says that differentiating ∑a_n(x−2)ⁿ with radius 5 must reduce the radius because the coefficients become n a_n. Which response is correct?

AThe radius remains 5; the factor n does not change the exponential rate that determines radius.

BThe radius becomes 4 because each exponent is lowered by 1.

CThe radius becomes 1/5 because coefficients are multiplied by n.

DThe derivative series has no radius of convergence.

Solution & Explanation:For power series, multiplying coefficients by n does not change the radius of convergence. The interior interval stays (−3,7), while endpoints still need separate tests.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Calculus II Math students. It aligns with educational standard AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55 (Select the derivative power series and its interval implications. Standards: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55.).