derivative of x^{sin(x})

解答

\frac{d}{d x} (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})

ma c l a u r in e^{- 3 x}

(f (x) (x^{2}))^{'}

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

s l o p e x y - 4 y^{2} = 8

\int 5 x^{3} d x