derivative of 5xarcsin(x)

解答

\frac{d}{d x} (5 x arcsin (x))

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

求解步骤

\frac{d}{d x} (5 x arcsin (x))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (x arcsin (x))

使用微分乘法定则:

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

f = x, g = arcsin (x)

= 5 (\frac{d x}{d x} arcsin (x) + \frac{d}{d x} (arcsin (x)) x)

\frac{d x}{d x} = 1

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

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

化简

5 (1 \cdot arcsin (x) + \frac{1}{1 - x ^{2}} x) : 5 (arcsin (x) + \frac{x}{1 - x ^{2}})

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

x \to \infty lim (0, x)

n = 1 \sum \infty \frac{2}{3} (\frac{1}{3})^{n}

\int \frac{1}{( x ^{2} + 2 x + 2 )} d x

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