derivative of sqrt(1-25x^2)arccos(5x)

解答

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

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

求解步骤

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

使用微分乘法定则:

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

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

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

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

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

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

化简

(- \frac{25 x}{1 - 25 x ^{2}}) arccos (5 x) + (- \frac{5}{1 - 25 x ^{2}}) 1 - 25 x^{2} : - \frac{25 x arccos ( 5 x )}{1 - 25 x ^{2}} - 5

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

x^{^{'}} = 2 (x + 1), x (0) = 0

\int cos (\frac{x y}{2}) d y

\int e^{- 0.01 x} d x

d er i v a t i v e 10 sin^{2} (x) + 10 cos^{2} (x)

t a y l or e^{- 4 x}