(\partial)/(\partial x)(x^2sin(x/y))

解答

\frac{\partial}{\partial x} (x^{2} sin (\frac{x}{y}))

2 x sin (\frac{x}{y}) + \frac{x ^{2} cos ( \frac{x}{y} )}{y}

求解步骤

\frac{\partial}{\partial x} (x^{2} sin (\frac{x}{y}))

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^{2}, g = sin (\frac{x}{y})

= \frac{\partial}{\partial x} (x^{2}) sin (\frac{x}{y}) + \frac{\partial}{\partial x} (sin (\frac{x}{y})) x^{2}

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (sin (\frac{x}{y})) = \frac{cos ( \frac{x}{y} )}{y}

= 2 x sin (\frac{x}{y}) + \frac{cos ( \frac{x}{y} )}{y} x^{2}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 2 x sin (\frac{x}{y}) + \frac{x ^{2} cos ( \frac{x}{y} )}{y}

\int_{0}^{1} 16 \frac{1}{x ^{p}} d x

t an g e n t x - x^{3} (1)

f (x) = \frac{1}{x} + 200

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

\frac{d}{d t} (\frac{t ^{2}}{10})