derivative of x^{9sin(x})

解

\frac{d}{d x} (x^{9 s i n (x)})

9 x^{9 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

解答ステップ

\frac{d}{d x} (x^{9 s i n (x)})

指数の規則を適用する:

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

x^{9 s i n (x)} = e^{9 s i n (x) l n (x)}

= \frac{d}{d x} (e^{9 s i n (x) l n (x)})

連鎖法則を適用:

e^{9 s i n (x) l n (x)} \frac{d}{d x} (9 sin (x) ln (x))

= e^{9 s i n (x) l n (x)} \frac{d}{d x} (9 sin (x) ln (x))

\frac{d}{d x} (9 sin (x) ln (x)) = 9 (cos (x) ln (x) + \frac{sin ( x )}{x})

= e^{9 s i n (x) l n (x)} \cdot 9 (cos (x) ln (x) + \frac{sin ( x )}{x})

e^{9 s i n (x) l n (x)} = x^{9 s i n (x)}

= 9 x^{9 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})