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

解

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

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

解答ステップ

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

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

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

簡素化

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