Differentiability

Easymathematics

The derivative of sin(x) is

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cos(x)

-cos(x)

sin(x)

-sin(x)

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About This Question

Subject: mathematics
Chapter: limit, continuity and differentiability
Topic: differentiability
Difficulty: Easy
Year: 2025

Solution

Correct Answer:

cos(x)

Definition of Derivative: $f^{'} (x) = lim_{h \to 0} \frac{s i n ( x + h ) - s i n x}{h}$ .
Trigonometric Identity: $sin (x + h) - sin x = 2 cos (x + \frac{h}{2}) sin (\frac{h}{2})$ .
Evaluate Limit: $f^{'} (x) = lim_{h \to 0} \frac{2 c o s ( x + \frac{h}{2} ) s i n ( \frac{h}{2} )}{h} = lim_{h \to 0} cos (x + \frac{h}{2}) \times \frac{s i n ( \frac{h}{2} )}{h /2}$ .
Standard result: $cos (x) \times 1 = cos x$ .

This easy difficulty mathematics question is from the chapter limit, continuity and differentiability, covering the topic of differentiability. It appeared in the 2025 exam.

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Differentiability

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