derivative of xe^{2x}(arcsin(3x))

解答

\frac{d}{d x} (x e^{2 x} (arcsin (3 x)))

e^{2 x} arcsin (3 x) + x (2 e^{2 x} arcsin (3 x) + \frac{3 e ^{2 x}}{1 - 9 x ^{2}})

求解步骤

\frac{d}{d x} (x e^{2 x} (arcsin (3 x)))

使用微分乘法定则:

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

f = x, g = e^{2 x} arcsin (3 x)

= \frac{d x}{d x} e^{2 x} arcsin (3 x) + \frac{d}{d x} (e^{2 x} arcsin (3 x)) x

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

\frac{d}{d x} (e^{2 x} arcsin (3 x)) = 2 e^{2 x} arcsin (3 x) + \frac{3 e ^{2 x}}{1 - 9 x ^{2}}

= 1 \cdot e^{2 x} arcsin (3 x) + (2 e^{2 x} arcsin (3 x) + \frac{3 e ^{2 x}}{1 - 9 x ^{2}}) x

化简

= e^{2 x} arcsin (3 x) + x (2 e^{2 x} arcsin (3 x) + \frac{3 e ^{2 x}}{1 - 9 x ^{2}})

1200 \frac{d y}{d x} = 12000 - 200 y - 1800

\int \frac{- 2}{x ^{6}} d x

t an g e n t f (x) = \frac{7 x}{x + 7}, (3, 2.1)

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

\int x 144 - x^{2} d x