derivative (1-25x^2)^2arcsin(5x)

解答

导数

(1 - 25 x^{2})^{2} arcsin (5 x)

- 100 x arcsin (5 x) (1 - 25 x^{2}) + 5 (- 25 x^{2} + 1)^{\frac{3}{2}}

求解步骤

\frac{d}{d x} ((1 - 25 x^{2})^{2} arcsin (5 x))

使用微分乘法定则:

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

f = (1 - 25 x^{2})^{2}, g = arcsin (5 x)

= \frac{d}{d x} ((1 - 25 x^{2})^{2}) arcsin (5 x) + \frac{d}{d x} (arcsin (5 x)) (1 - 25 x^{2})^{2}

\frac{d}{d x} ((1 - 25 x^{2})^{2}) = - 100 x (1 - 25 x^{2})

\frac{d}{d x} (arcsin (5 x)) = \frac{5}{1 - 25 x ^{2}}

= (- 100 x (1 - 25 x^{2})) arcsin (5 x) + \frac{5}{1 - 25 x ^{2}} (1 - 25 x^{2})^{2}

化简

(- 100 x (1 - 25 x^{2})) arcsin (5 x) + \frac{5}{1 - 25 x ^{2}} (1 - 25 x^{2})^{2} : - 100 x arcsin (5 x) (1 - 25 x^{2}) + 5 (- 25 x^{2} + 1)^{\frac{3}{2}}

= - 100 x arcsin (5 x) (1 - 25 x^{2}) + 5 (- 25 x^{2} + 1)^{\frac{3}{2}}

t an g e n t \frac{64}{x ^{2} + 16}, at x = 3

\int_{2}^{3} (x^{2} - 4) d x

t an g e n t f (x) = \frac{6 x}{2 + x ^{2}}, (2, 2)

\int (3 x + 2) d x

d er i v a t i v e y = 19 cos (\frac{x}{b} - 2.5) + 19