derivative of e^{cos(x}+e^{sin(y)})

解

\frac{d}{d x} (e^{c o s (x)} + e^{s i n (y)})

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

解答ステップ

\frac{d}{d x} (e^{c o s (x)} + e^{s i n (y)})

和/差の法則を適用:

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

= \frac{d}{d x} (e^{c o s (x)}) + \frac{d}{d x} (e^{s i n (y)})

\frac{d}{d x} (e^{c o s (x)}) = - e^{c o s (x)} sin (x)

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

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