derivative e^{sin(x)}cos(x)

解

導関数

e^{s i n (x)} cos (x)

e^{s i n (x)} cos^{2} (x) - e^{s i n (x)} sin (x)

解答ステップ

\frac{d}{d x} (e^{s i n (x)} cos (x))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{s i n (x)}, g = cos (x)

= \frac{d}{d x} (e^{s i n (x)}) cos (x) + \frac{d}{d x} (cos (x)) e^{s i n (x)}

\frac{d}{d x} (e^{s i n (x)}) = e^{s i n (x)} cos (x)

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

= e^{s i n (x)} cos (x) cos (x) + (- sin (x)) e^{s i n (x)}

簡素化

e^{s i n (x)} cos (x) cos (x) + (- sin (x)) e^{s i n (x)} : e^{s i n (x)} cos^{2} (x) - e^{s i n (x)} sin (x)

= e^{s i n (x)} cos^{2} (x) - e^{s i n (x)} sin (x)