Find the derivative of $f(x) = \sin x$ with respect to $x$ using first principles.
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Question

Find the derivative of $f(x) = \sin x$ with respect to $x$ using first principles.

Accepted Answer

By definition, derivative is $\lim{h 	o 0} \frac{\sin(x+h) - \sin x}{h}$. Using $\sin A - \sin B = 2 \cos\frac{A+B}{2}\sin\frac{A-B}{2}$, the limit simplifies to $\cos x$.

Limits and Derivatives

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