(\partial)/(\partial x)((q(x,r,s,t)x+r)/(sx+t))

解答

\frac{\partial}{\partial x} (\frac{q ( x , r , s , t ) x + r}{s x + t})

\frac{( ( \frac{\partial}{\partial x} ( q ( x , r , s , t ) ) x + 1 \cdot q ( x , r , s , t ) ) + 0 ) ( s x + t ) - s ( q ( x , r , s , t ) x + r )}{( s x + t ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{q ( x , r , s , t ) x + r}{s x + t})

将

r, s, t

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 x} ( q ( x , r , s , t ) x + r ) ( s x + t ) - \frac{\partial}{\partial x} ( s x + t ) ( q ( x , r , s , t ) x + r )}{( s x + t ) ^{2}}

\frac{\partial}{\partial x} (q (x, r, s, t) x + r) = (\frac{\partial}{\partial x} (q (x, r, s, t)) x + 1 \cdot q (x, r, s, t)) + 0

\frac{\partial}{\partial x} (s x + t) = s

= \frac{( ( \frac{\partial}{\partial x} ( q ( x , r , s , t ) ) x + 1 \cdot q ( x , r , s , t ) ) + 0 ) ( s x + t ) - s ( q ( x , r , s , t ) x + r )}{( s x + t ) ^{2}}

\frac{d}{d x} (x - \frac{2}{x})

t an g e n t f (x) = x^{3} - 6 x, (2, - 4)

\int_{- 1}^{3} (2 x^{2} + 1) d x

\frac{\partial}{\partial y} (ln (x^{3} + y^{4}))

\frac{\partial}{\partial t} (r sin (t))