NCERT · Class 11 · Mathematics · Limits and DerivativesFind the derivative of $f(x) = \sin x$ with respect to $x$ using first principles.
Step-by-Step Solution
By definition, derivative is $\lim_{h \to 0} \frac{\sin(x+h) - \sin x}{h}$. Using $\sin A - \sin B = 2 \cos\frac{A+B}{2}\sin\frac{A-B}{2}$, the limit simplifies to $\cos x$.
Detailed Options Breakdown
Option : cos x (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: -cos x
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Limits and Derivatives.
Option 2: sin x
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Limits and Derivatives.
Option 3: -sin x
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Limits and Derivatives.
💡 Study Guide: This question tests core syllabus concepts from Limits and Derivatives. For formulas, key summaries, and mock exam reference guides, read the full Limits and Derivatives Revision Notes.