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Differentiation Of Exponential and Logarithmic Functions — Revision Notes

Telangana Open School (TOSS) · Class 12 · Mathematics

Differentiation Of Exponential and Logarithmic Functions revision notes for Telangana Open School (TOSS) Class 12 Mathematics: 3 topics in quick points.

52 questions25 flashcards8 formulas & key relations5 concepts

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Key Topics to Revise

1

Derivatives of Exponential Functions

  • The derivative of \( e^x \) is \( e^x \).
  • For \( e^{f(x)} \), use chain rule: derivative is \( e^{f(x)} \cdot f'(x) \).
  • Derivative of \( a^x \) is \( a^x \log a \), where \( a > 0 \).
2

Derivatives of Logarithmic Functions

  • The derivative of \( \log x \) is \( \frac{1}{x} \).
  • For \( \log(f(x)) \), derivative is \( \frac{1}{f(x)} \cdot f'(x) \).
  • Use logarithmic differentiation for functions of the form \( [f(x)]^{g(x)} \).
3

Second Order Derivatives

  • Second derivative is the derivative of the first derivative.
  • Denoted as \( \frac{d^2y}{dx^2} \) or \( f''(x) \).
  • Used to determine concavity and acceleration in physical applications.

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Full Notes

Key Concepts

The derivative of \( e^x \)For any positive constant \(The derivative of \( \log xWhen differentiating functions of the formThe second derivative is obtained by

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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