derivative y=x^{5sin(x)}

解答

导数

y = x^{5 s i n (x)}

5 x^{5 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

求解步骤

\frac{d}{d x} (x^{5 s i n (x)})

使用指数法则:

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

x^{5 s i n (x)} = e^{5 s i n (x) l n (x)}

= \frac{d}{d x} (e^{5 s i n (x) l n (x)})

使用连锁律:

e^{5 s i n (x) l n (x)} \frac{d}{d x} (5 sin (x) ln (x))

= e^{5 s i n (x) l n (x)} \frac{d}{d x} (5 sin (x) ln (x))

\frac{d}{d x} (5 sin (x) ln (x)) = 5 (cos (x) ln (x) + \frac{sin ( x )}{x})

= e^{5 s i n (x) l n (x)} \cdot 5 (cos (x) ln (x) + \frac{sin ( x )}{x})

e^{5 s i n (x) l n (x)} = x^{5 s i n (x)}

= 5 x^{5 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

\int \frac{x \cdot arcsin ( x )}{1 - x ^{2}} d x

d er i v a t i v e - x e^{- x} + e^{- x}

\frac{d}{d x} (2 e^{x} + e^{x} x)

y^{^{'}} = 20 x y

\frac{d}{d x} (\frac{x}{x - 6})