sinの微分

$ f'(x) = \lim_{a \to 0}{f(x+a) - f(x) \over (x+a) - x}

$ f'(x) = \lim_{a \to 0}{\sin(x+a) - \sin x \over (x+a) - x}

$ \sin(x+a) = \sin x \cos a + \cos x \sin a

$ f'(x) = \lim_{a \to 0}{\sin x \cos a + \cos x \sin a - \sin x \over a}

$ f'(x) = \lim_{a \to 0} \bigg\lparen {{\sin x \cdot {\cos a - 1 \over a}} + {\cos x \cdot {\sin a \over a}}} \bigg\rparen