Find the derivative of sin x at x=0. | vedclass

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(B) Let $f(x) = \sin x$. Then,the derivative at $x=0$ is given by $f'(0) = \lim_{h 	o 0} \frac{f(0+h) - f(0)}{h}$. Substituting $f(x) = \sin x$,we ge

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$1$

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(B) Let $f(x) = \sin x$. Then,the derivative at $x=0$ is given by $f'(0) = \lim_{h 	o 0} \frac{f(0+h) - f(0)}{h}$. Substituting $f(x) = \sin x$,we get $f'(0) = \lim_{h 	o 0} \frac{\sin(0+h) - \sin(0)}{h}$. Since $\sin(0) = 0$,this simplifies to $f'(0) = \lim_{h 	o 0} \frac{\sin h}{h}$. Using the standard limit $\lim_{h 	o 0} \frac{\sin h}{h} = 1$,we find $f'(0) = 1$.

Find the derivative of $\sin x$ at $x=0$.

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