derivative of x^{7sin(x})

解

\frac{d}{d x} (x^{7 s i n (x)})

7 x^{7 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

解答ステップ

\frac{d}{d x} (x^{7 s i n (x)})

指数の規則を適用する:

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

x^{7 s i n (x)} = e^{7 s i n (x) l n (x)}

= \frac{d}{d x} (e^{7 s i n (x) l n (x)})

連鎖法則を適用:

e^{7 s i n (x) l n (x)} \frac{d}{d x} (7 sin (x) ln (x))

= e^{7 s i n (x) l n (x)} \frac{d}{d x} (7 sin (x) ln (x))

\frac{d}{d x} (7 sin (x) ln (x)) = 7 (cos (x) ln (x) + \frac{sin ( x )}{x})

= e^{7 s i n (x) l n (x)} \cdot 7 (cos (x) ln (x) + \frac{sin ( x )}{x})

e^{7 s i n (x) l n (x)} = x^{7 s i n (x)}

= 7 x^{7 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})