(\partial)/(\partial t)((3s+t)/(4s-t))

解答

\frac{\partial}{\partial t} (\frac{3 s + t}{4 s - t})

\frac{7 s}{( 4 s - t ) ^{2}}

求解步骤

\frac{\partial}{\partial t} (\frac{3 s + t}{4 s - t})

将

s

视为常数

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{\partial}{\partial t} ( 3 s + t ) ( 4 s - t ) - \frac{\partial}{\partial t} ( 4 s - t ) ( 3 s + t )}{( 4 s - t ) ^{2}}

\frac{\partial}{\partial t} (3 s + t) = 1

\frac{\partial}{\partial t} (4 s - t) = - 1

= \frac{1 \cdot ( 4 s - t ) - ( - 1 ) ( 3 s + t )}{( 4 s - t ) ^{2}}

化简

\frac{1 \cdot ( 4 s - t ) - ( - 1 ) ( 3 s + t )}{( 4 s - t ) ^{2}} : \frac{7 s}{( 4 s - t ) ^{2}}

= \frac{7 s}{( 4 s - t ) ^{2}}

2 y cos (x) d x + 3 sin (x) d y = 0

\int \frac{y}{x ^{2} + y ^{2}} d y

\frac{\partial}{\partial x} (x y^{2} - y x^{3})

\frac{d}{d x} (1 + 40 x^{3} - 3 x^{5})

x \to 2 lim (1680 x^{3} - 120 x)