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Differentiation Of Exponential and Logarithmic Functions — Flashcards

Telangana Open School (TOSS) · Class 12 · Mathematics

25 flashcards for Differentiation Of Exponential and Logarithmic Functions (Telangana Open School (TOSS) Class 12 Mathematics) to test yourself on key.

52 questions25 flashcards8 formulas & key relations5 concepts

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25 Flashcards·
Exponential DerivativesLogarithmic DerivativesProduct Rule with ExponentialsQuotient Rule with Exponentials
Card 1Exponential Derivatives

Differentiate: \( y = e^{3x} \)

Answer

Step 1: Use the rule \( \frac{d}{dx}(e^{u}) = e^{u} \cdot \frac{du}{dx} \) Step 2: Here, \( u = 3x \), so \( \frac{du}{dx} = 3 \) Step 3: \( \frac{dy}{dx} = e^{3x} \cdot 3 = 3e^{3x} \) Answer: \( \…

Card 2Exponential Derivatives

Differentiate: \( y = e^{x^2} \)

Answer

Step 1: Let \( u = x^2 \), so \( \frac{du}{dx} = 2x \) Step 2: Use \( \frac{d}{dx}(e^u) = e^u \cdot \frac{du}{dx} \) Step 3: \( \frac{dy}{dx} = e^{x^2} \cdot 2x = 2x e^{x^2} \) Answer: \( \frac{dy}…

Card 3Logarithmic Derivatives

Differentiate: \( y = \log(5x + 2) \)

Answer

Step 1: Use \( \frac{d}{dx}(\log u) = \frac{1}{u} \cdot \frac{du}{dx} \) Step 2: \( u = 5x + 2 \), so \( \frac{du}{dx} = 5 \) Step 3: \( \frac{dy}{dx} = \frac{1}{5x+2} \cdot 5 = \frac{5}{5x+2} \) A…

Card 4Logarithmic Derivatives

Differentiate: \( y = \log(\sin x) \)

Answer

Step 1: Let \( u = \sin x \), so \( \frac{du}{dx} = \cos x \) Step 2: \( \frac{d}{dx}(\log u) = \frac{1}{u} \cdot \frac{du}{dx} \) Step 3: \( \frac{dy}{dx} = \frac{1}{\sin x} \cdot \cos x = \cot x \…

Card 5Exponential Derivatives

Differentiate: \( y = e^{\sqrt{x}} \)

Answer

Step 1: Let \( u = \sqrt{x} = x^{1/2} \), so \( \frac{du}{dx} = \frac{1}{2\sqrt{x}} \) Step 2: \( \frac{dy}{dx} = e^{\sqrt{x}} \cdot \frac{1}{2\sqrt{x}} \) Answer: \( \frac{dy}{dx} = \frac{e^{\sqrt{…

Card 6Logarithmic Derivatives

Differentiate: \( y = \log(\log x) \)

Answer

Step 1: Let \( u = \log x \), so \( \frac{du}{dx} = \frac{1}{x} \) Step 2: \( \frac{d}{dx}(\log u) = \frac{1}{u} \cdot \frac{du}{dx} \) Step 3: \( \frac{dy}{dx} = \frac{1}{\log x} \cdot \frac{1}{x} …

Card 7Product Rule with Exponentials

Differentiate: \( y = x e^x \)

Answer

Step 1: Use product rule: \( (uv)' = u'v + uv' \) Let \( u = x \), \( v = e^x \) Step 2: \( u' = 1 \), \( v' = e^x \) Step 3: \( \frac{dy}{dx} = 1 \cdot e^x + x \cdot e^x = e^x(1 + x) \) Answer: \…

Card 8Quotient Rule with Exponentials

Differentiate: \( y = \frac{e^x}{x} \)

Answer

Step 1: Use quotient rule: \( \left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2} \) Let \( u = e^x \), \( v = x \) Step 2: \( u' = e^x \), \( v' = 1 \) Step 3: \( \frac{dy}{dx} = \frac{e^x \cdot 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 many flashcards are available for Differentiation Of Exponential and Logarithmic Functions?
There are 25 flashcards for Differentiation Of Exponential and Logarithmic Functions covering key definitions, facts and ideas. A few sample cards are shown on this page.
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.

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