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

解

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

- sin (x^{s i n (x)}) x^{s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

解答ステップ

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

連鎖法則を適用:

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

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

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

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