(\partial)/(\partial x)(ysin(y/x))

解答

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

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

求解步骤

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

将

y

视为常数

将常数提出:

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

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

使用连锁律:

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

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

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

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

化简

y cos (\frac{y}{x}) (- \frac{y}{x ^{2}}) : - \frac{y ^{2} cos ( \frac{y}{x} )}{x ^{2}}

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

x \to - 4 lim (5 x + 2)

x \to - 2 lim (\frac{( 3 )}{( x + 2 )})

\int_{0}^{6} \frac{π}{4} (36 - y^{2}) d y

\int_{0}^{1} 34.6 e^{- 0.06 t} d t

\int_{0}^{0.15} x d x