(\partial)/(\partial x)(x*arcsin(y/x))

解答

\frac{\partial}{\partial x} (x \cdot arcsin (\frac{y}{x}))

arcsin (\frac{y}{x}) - \frac{y}{x ^{2} - y ^{2}}

求解步骤

\frac{\partial}{\partial x} (x arcsin (\frac{y}{x}))

将

y

视为常数

使用微分乘法定则:

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

f = x, g = arcsin (\frac{y}{x})

= \frac{\partial}{\partial x} (x) arcsin (\frac{y}{x}) + \frac{\partial}{\partial x} (arcsin (\frac{y}{x})) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (arcsin (\frac{y}{x})) = - \frac{y}{x x ^{2} - y ^{2}}

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

化简

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

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

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

\frac{\partial}{\partial x} (- 2 tan (x) sin (2 y))

\frac{d}{d x} (- A e^{- x})

\frac{d}{d x} (ln (g (x) (3 x^{2})))

\frac{d}{d x} (e^{2 x} sin (x))