Differentiation
ICSE · Class 11 · Mathematics
Practice quiz for Differentiation — ICSE Class 11 Mathematics. MCQs and questions with answers to test your preparation.
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The derivative of f(x) = c (constant) is:
d/dx(x⁵) equals:
d/dx(sin x) equals:
d/dx(cos x) equals:
Sample Questions
The first principle of differentiation states that f'(x) equals:
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lim_{h→0} [f(x+h)−f(x)]/h
First principle: f'(x) = lim_{h→0} [f(x+h)−f(x)]/h. This is the definition of derivative.
The derivative of f(x) = x at x = 1 is:
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1
f'(x) = lim_{h→0} [(x+h)−x]/h = 1. So f'(1) = 1.
Geometrically, f'(a) represents:
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Slope of tangent to curve y=f(x) at x=a
The derivative f'(a) equals the slope of the tangent line to the curve y = f(x) at (a, f(a)).
d/dx(tan x) equals:
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sec²x
Standard result: d/dx(tan x) = sec²x.
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