derivative x^{sin^2(x)}

解答

导数

x^{s i n^{2} (x)}

x^{s i n^{2} (x)} (sin (2 x) ln (x) + \frac{sin ^{2} ( x )}{x})

求解步骤

\frac{d}{d x} (x^{s i n^{2} (x)})

使用指数法则:

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

x^{s i n^{2} (x)} = e^{s i n^{2} (x) l n (x)}

= \frac{d}{d x} (e^{s i n^{2} (x) l n (x)})

使用连锁律:

e^{s i n^{2} (x) l n (x)} \frac{d}{d x} (sin^{2} (x) ln (x))

= e^{s i n^{2} (x) l n (x)} \frac{d}{d x} (sin^{2} (x) ln (x))

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

= e^{s i n^{2} (x) l n (x)} (sin (2 x) ln (x) + \frac{sin ^{2} ( x )}{x})

e^{s i n^{2} (x) l n (x)} = x^{s i n^{2} (x)}

= x^{s i n^{2} (x)} (sin (2 x) ln (x) + \frac{sin ^{2} ( x )}{x})

d er i v a t i v e e^{x^{2} + y^{2}}

d er i v a t i v e y = - 10 x + 7

d er i v a t i v e \frac{1 - e ^{x}}{1 + e ^{x}}

d er i v a t i v e 2 + x

d er i v a t i v e \frac{1}{( 1 + x )}