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Differentiation Of Exponential and Logarithmic Functions — Study Plan

Telangana Open School (TOSS) · Class 12 · Mathematics

A step-by-step study plan for Differentiation Of Exponential and Logarithmic Functions, Telangana Open School (TOSS) Class 12 Mathematics: what to learn.

52 questions25 flashcards8 formulas & key relations5 concepts

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Study Plan

1
Day 1–2

Learn the Theory

Read the textbook chapter carefully. Note down definitions, formulas and key ideas. Focus on: Derivatives of Exponential Functions, Derivatives of Logarithmic Functions, Second Order Derivatives.

2
Day 3

Practise

Solve the textbook exercises and extra practice questions. There are 52 questions available for this chapter.

3
Day 4

Revise & Test

Revise key points without looking at your notes. Take a practice quiz and mark weak areas for another pass.

4
Day 7

Spaced Revision

Come back to Differentiation Of Exponential and Logarithmic Functions after a week. Use flashcards for quick recall and try past exam questions on this chapter.

What to Focus On

  • The derivative of \( e^x \) is \( e^x \)
  • For \( e^{f(x)} \), the derivative is \( e^{f(x)} \cdot f'(x) \)
  • For \( a^x \), use logarithmic differentiation or the standard formula
  • Derivative of \( \log x \) is \( \frac{1}{x} \)
  • Chain rule applies when differentiating \( \log(f(x)) \)
  • Logarithmic differentiation simplifies derivatives of products, quotients, and powers
  • Use logarithmic differentiation for \( f(x)^{g(x)} \)
  • Take log on both sides before differentiating
  • Apply product rule after taking log

Common Mistakes to Avoid

The derivative of \( e^x \) is \( x e^{x-1} \), just like power rule for \( x^n \).

The derivative of \( a^x \) is \( x a^{x-1} \), same as power rule.

The derivative of \( \log x \) is \( \frac{1}{x \log 10} \), always involving base 10.

Memory Tips

Derivative of e^x is e^x

Chain rule with e^(f(x))

d/dx(a^x) = a^x ln a

Derivative of log x is 1/x

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Frequently Asked Questions

What are the important topics in Differentiation Of Exponential and Logarithmic Functions for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Differentiation Of Exponential and Logarithmic Functions include Derivatives of Exponential Functions, Derivatives of Logarithmic Functions, Second Order Derivatives. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Differentiation Of Exponential and Logarithmic Functions for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 52 practice questions on Differentiation Of Exponential and Logarithmic Functions. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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