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

解答

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

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

求解步骤

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

将

r

视为常数

使用连锁律:

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

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

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

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

化简

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

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

\int e^{x} 25 - e^{2 x} d x

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