derivative x^{tan(x)}

解

導関数

x^{t a n (x)}

e^{t a n (x) l n (x)} (sec^{2} (x) ln (x) + \frac{tan ( x )}{x})

解答ステップ

\frac{d}{d x} (x^{t a n (x)})

指数の規則を適用する:

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

x^{t a n (x)} = e^{t a n (x) l n (x)}

= \frac{d}{d x} (e^{t a n (x) l n (x)})

連鎖法則を適用:

e^{t a n (x) l n (x)} \frac{d}{d x} (tan (x) ln (x))

= e^{t a n (x) l n (x)} \frac{d}{d x} (tan (x) ln (x))

\frac{d}{d x} (tan (x) ln (x)) = sec^{2} (x) ln (x) + \frac{tan ( x )}{x}

= e^{t a n (x) l n (x)} (sec^{2} (x) ln (x) + \frac{tan ( x )}{x})