derivative x^{11}arccos(x)

解答

导数

x^{11} arccos (x)

11 x^{10} arccos (x) - \frac{x ^{11}}{1 - x ^{2}}

求解步骤

\frac{d}{d x} (x^{11} arccos (x))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{11}, g = arccos (x)

= \frac{d}{d x} (x^{11}) arccos (x) + \frac{d}{d x} (arccos (x)) x^{11}

\frac{d}{d x} (x^{11}) = 11 x^{10}

\frac{d}{d x} (arccos (x)) = - \frac{1}{1 - x ^{2}}

= 11 x^{10} arccos (x) + (- \frac{1}{1 - x ^{2}}) x^{11}

化简

11 x^{10} arccos (x) + (- \frac{1}{1 - x ^{2}}) x^{11} : 11 x^{10} arccos (x) - \frac{x ^{11}}{1 - x ^{2}}

= 11 x^{10} arccos (x) - \frac{x ^{11}}{1 - x ^{2}}

t an g e n t g (x) = e^{x^{5}}, (- 1, \frac{1}{e})

\frac{\partial}{\partial x} (2 ln (x))

b \to \infty lim (b c)

\int \frac{1}{5 + 3 x ^{2}} d x

\frac{d y}{d x} = \frac{1}{2} x + 1