derivative f(x)=sin(x)-1/3 sin(3x)+1/5 sin(5x)

解

導関数

f (x) = sin (x) - \frac{1}{3} sin (3 x) + \frac{1}{5} sin (5 x)

cos (x) - cos (3 x) + cos (5 x)

解答ステップ

\frac{d}{d x} (sin (x) - \frac{1}{3} sin (3 x) + \frac{1}{5} sin (5 x))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sin (x)) - \frac{d}{d x} (\frac{1}{3} sin (3 x)) + \frac{d}{d x} (\frac{1}{5} sin (5 x))

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (\frac{1}{3} sin (3 x)) = cos (3 x)

\frac{d}{d x} (\frac{1}{5} sin (5 x)) = cos (5 x)

= cos (x) - cos (3 x) + cos (5 x)