(\partial)/(\partial s)(rln(r^2+s^2))

解答

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

\frac{2 rs}{r ^{2} + s ^{2}}

求解步骤

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

将

r

视为常数

将常数提出:

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

= r \frac{\partial}{\partial s} (ln (r^{2} + s^{2}))

使用连锁律:

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

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

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

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

化简

r \frac{1}{r ^{2} + s ^{2}} \cdot 2 s : \frac{2 rs}{r ^{2} + s ^{2}}

= \frac{2 rs}{r ^{2} + s ^{2}}

\frac{d}{d x} (\frac{80}{x})

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