derivative of x^{-2cos(x})

解

\frac{d}{d x} (x^{- 2 c o s (x)})

x^{- 2 c o s (x)} (2 sin (x) ln (x) - \frac{2 cos ( x )}{x})

解答ステップ

\frac{d}{d x} (x^{- 2 c o s (x)})

指数の規則を適用する:

a^{b} = e^{b l n (a)}

x^{- 2 c o s (x)} = e^{(- 2 c o s (x)) l n (x)}

= \frac{d}{d x} (e^{(- 2 c o s (x)) l n (x)})

連鎖法則を適用:

e^{(- 2 c o s (x)) l n (x)} \frac{d}{d x} ((- 2 cos (x)) ln (x))

= e^{(- 2 c o s (x)) l n (x)} \frac{d}{d x} ((- 2 cos (x)) ln (x))

\frac{d}{d x} ((- 2 cos (x)) ln (x)) = 2 sin (x) ln (x) - \frac{2 cos ( x )}{x}

= e^{(- 2 c o s (x)) l n (x)} (2 sin (x) ln (x) - \frac{2 cos ( x )}{x})

簡素化

e^{(- 2 c o s (x)) l n (x)} (2 sin (x) ln (x) - \frac{2 cos ( x )}{x}) : x^{- 2 c o s (x)} (2 sin (x) ln (x) - \frac{2 cos ( x )}{x})

= x^{- 2 c o s (x)} (2 sin (x) ln (x) - \frac{2 cos ( x )}{x})