(\partial)/(\partial s)(ln(1+s^2+t^2))

解答

\frac{\partial}{\partial s} (ln (1 + s^{2} + t^{2}))

\frac{2 s}{1 + s ^{2} + t ^{2}}

求解步骤

\frac{\partial}{\partial s} (ln (1 + s^{2} + t^{2}))

将

t

视为常数

使用连锁律:

\frac{1}{1 + s ^{2} + t ^{2}} \frac{\partial}{\partial s} (1 + s^{2} + t^{2})

= \frac{1}{1 + s ^{2} + t ^{2}} \frac{\partial}{\partial s} (1 + s^{2} + t^{2})

\frac{\partial}{\partial s} (1 + s^{2} + t^{2}) = 2 s

= \frac{1}{1 + s ^{2} + t ^{2}} \cdot 2 s

化简

\frac{1}{1 + s ^{2} + t ^{2}} \cdot 2 s : \frac{2 s}{1 + s ^{2} + t ^{2}}

= \frac{2 s}{1 + s ^{2} + t ^{2}}