derivative y=x^{sin(x)}

解答

导数

y = x^{s i n (x)}

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

求解步骤

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

使用指数法则:

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

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

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

使用连锁律:

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

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

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

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

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

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