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Differentiation — Flashcards

ICSE · Class 11 · Mathematics

32 flashcards for Differentiation (ICSE Class 11 Mathematics) to test yourself on key terms and facts. Sample: "Find the derivative of f(x) = x at x = 1"

60 questions32 flashcards21 formulas & key relations5 concepts

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A graph of a function y=f(x) with a tangent line at a point (x, y), illustrating dy/dx as the slope of the tangent.
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32 Flashcards·
Derivative by first principleLinear function derivativePolynomial derivative by definitionConstant multiple with quadraticQuadratic derivative by definitionChecking values of derivativeTrigonometric derivative by definition
Card 1Derivative by first principle

Find the derivative of f(x) = x at x = 1 using first principle.

Answer

Step 1: Use f'(x) = lim h→0 [f(x+h) - f(x)] / h. Step 2: Here, f(1+h) = 1+h and f(1) = 1. Step 3: f'(1) = lim h→0 [(1+h) - 1] / h = lim h→0 [h/h] = lim h→0 [1] = 1. Answer: 1…

Card 2Linear function derivative

Find the derivative of f(x) = 99x at x = 100 using first principle.

Answer

Step 1: Use f'(x) = lim h→0 [f(x+h) - f(x)] / h. Step 2: f(100+h) = 99(100+h) and f(100) = 9900. Step 3: f'(100) = lim h→0 [99(100+h) - 9900] / h = lim h→0 [99h/h] = 99. Answer: 99…

Card 3Polynomial derivative by definition

Solve: If f(x) = x^2 - 2, find f'(10).

Answer

Step 1: Use f'(x) = lim h→0 [f(x+h) - f(x)] / h. Step 2: f(10+h) = (10+h)^2 - 2 = 100 + 20h + h^2 - 2. Step 3: f(10) = 10^2 - 2 = 98. Step 4: f'(10) = lim h→0 [(100 + 20h + h^2 - 2) - 98] / h = lim h→…

Card 4Constant multiple with quadratic

Solve: If f(x) = kx^2, find f'(2).

Answer

Step 1: Use f'(x) = lim h→0 [f(x+h) - f(x)] / h. Step 2: f(2+h) = k(2+h)^2 = k(4 + 4h + h^2). Step 3: f(2) = 4k. Step 4: f'(2) = lim h→0 [k(4 + 4h + h^2) - 4k] / h = lim h→0 [k(4h + h^2)]/h = lim h→0 …

Card 5Quadratic derivative by definition

Solve: For f(x) = 2x^2 + 3x - 5, find f'(-1).

Answer

Step 1: Use f'(x) = lim h→0 [f(x+h) - f(x)] / h. Step 2: f(-1+h) = 2(-1+h)^2 + 3(-1+h) - 5. Step 3: Expand: 2(1 - 2h + h^2) - 3 + 3h - 5 = -6 - h + 2h^2. Step 4: f(-1) = 2(1) - 3 - 5 = -6. Step 5: f'(…

Card 6Checking values of derivative

Apply the result for f(x) = 2x^2 + 3x - 5 to find f'(0), then verify f'(0) + 3f'(-1).

Answer

Step 1: Differentiate f(x) = 2x^2 + 3x - 5. Step 2: f'(x) = 4x + 3. Step 3: f'(0) = 3. Step 4: From the previous result, f'(-1) = -1. Step 5: f'(0) + 3f'(-1) = 3 + 3(-1) = 0. Answer: f'(0) = 3 and f'(…

Card 7Trigonometric derivative by definition

Find the derivative of f(x) = sin x at x = 0 using first principle.

Answer

Step 1: f'(0) = lim h→0 [sin(0+h) - sin 0] / h. Step 2: This becomes lim h→0 [sin h / h]. Step 3: The limit equals 1. Answer: 1…

Card 8Trigonometric derivative by definition

Find the derivative of f(x) = cos 2x at x = π/2 using first principle.

Answer

Step 1: f'(π/2) = lim h→0 [cos(2(π/2 + h)) - cos(π)] / h. Step 2: This becomes lim h→0 [cos(π + 2h) + 1] / h. Step 3: Since cos(π + 2h) = -cos 2h, the expression is lim h→0 [1 - cos 2h] / h. Step 4: T…

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Frequently Asked Questions

What are the important topics in Differentiation for ICSE Class 11 Mathematics?
Key topics in Differentiation include Differentiability at a Point, First Principle and Meaning of Derivative, Basic Rules of Differentiation, Standard Derivatives and Special Results. Study these first, then practise questions on each for Class 11 exams.
How many flashcards are available for Differentiation?
There are 32 flashcards for Differentiation covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Differentiation for Class 11 exams?
Learn the core ideas first, then work through the 60 practice questions on Differentiation. Revise definitions regularly and use flashcards for quick recall before the exam.

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