What is (\partial)/(\partial s)(rln(r^2+s^2)) ?

The answer to (\partial)/(\partial s)(rln(r^2+s^2)) is (2rs)/(r^2+s^2)

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

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

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

Solution steps

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

Treat

r

as a constant

Take the constant out:

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

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

Apply the chain rule:

\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

Simplify

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

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

What is (\partial)/(\partial s)(rln(r^2+s^2)) ?
The answer to (\partial)/(\partial s)(rln(r^2+s^2)) is (2rs)/(r^2+s^2)